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Dissertations / Theses on the topic 'Latin squares'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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1

Rhodes, Susan Jane. "Latin squares with restrictions." Thesis, Lancaster University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385954.

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2

Ghebremicael, Aman W. "Latin squares and applications /." Available to subscribers only, 2009. http://proquest.umi.com/pqdweb?did=1791777361&sid=1&Fmt=2&clientId=1509&RQT=309&VName=PQD.

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Thesis (Ph. D.)--Southern Illinois University Carbondale, 2009.<br>"Department of Mathematics." Keywords: Intercalates, Latin squares. Includes bibliographical references (p. 43-44). Also available online.
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3

Ghebremicael, Aman. "Latin Squares and Applications." OpenSIUC, 2008. https://opensiuc.lib.siu.edu/dissertations/266.

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Intercalates and the maximum number of intercalates are presented. We introduced partially intercalate complete Latin squares and results on the existence of some infinite families as well as Latin squares of smaller size is given. The second part of our work summarizes the main results on orthogonal Latin squares. Special type of Latin squares, gerechte designs, are introduced and proof for the existence of such orthogonal Latin squares of prime orders is also presented.
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4

James, Fiedler. "Greco-Latin squares as bijections." [Ames, Iowa : Iowa State University], 2007.

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5

Whitaker, Roger Marcus. "Mutually quasi-orthogonal Latin squares." Thesis, Keele University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.311129.

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This thesis considers problems concerning Latin squares and sets of mutually quasiorthogonal Latin squares (MQOLS). We show how MQOLS are related to a number of other designs and establish bounds on Nq(n), the maximum number of Latin squares of order n in a mutually quasi-orthogonal set. We report the number of quasi-complete mappings admitted by each group of order 15 or less, and explain the surprising result that each of the non-cyclic groups of order 8 possesses exactly 384 complete mappings. For each group G of order 15 or less, we identify the sizes of all maximal sets of mutually orthog
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6

Isaksson, Edward. "Latin Squares and Tactical Configurations." Thesis, Uppsala universitet, Algebra och geometri, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-447463.

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7

Daqqa, Ibtisam. "Subconstituent algebras of Latin squares." [Tampa, Fla] : University of South Florida, 2008. http://purl.fcla.edu/usf/dc/et/SFE0002395.

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8

Daqqa, Ibtisam. "Subconstituent Algebras of Latin Squares." Scholar Commons, 2007. https://scholarcommons.usf.edu/etd/199.

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Let n be a positive integer. A Latin square of order n is an n×n array L such that each element of some n-set occurs in each row and in each column of L exactly once. It is well-known that one may construct a 4-class association scheme on the positions of a Latin square, where the relations are the identity, being in the same row, being in the same column, having the same entry, and everything else. We describe the subconstituent (Terwilliger) algebras of such an association scheme. One also may construct several strongly regular graphs on the positions of a Latin square, where adjacency corre
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9

Casselgren, Carl Johan, and Roland Häggkvist. "Completing partial Latin squares with one filled row, column and symbol." Linköpings universitet, Matematik och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-92689.

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Let P be an n×n partial Latin square every non-empty cell of which lies in a fixed row r, a fixed column c or contains a fixed symbol s. Assume further that s is the symbol of cell (r,c) in P. We prove that P is completable to a Latin square if n≥8 and n is divisible by 4, or n≤7 and n∉{3,4,5}. Moreover, we present a polynomial algorithm for the completion of such a partial Latin square.
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10

Andrén, Lina J. "On Latin squares and avoidable arrays." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-36040.

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This thesis consists of the four papers listed below and a survey of the research area. I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k II Lina J. Andrén: Avoidability of random arrays III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such
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11

Higham, Jeffrey T. "Construction methods for row-complete Latin squares." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq21356.pdf.

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12

Gunawardana, Beruwalage Lakshika Kumari. "A VARIATION ON MUTUALLY ORTHOGONAL LATIN SQUARES." OpenSIUC, 2016. https://opensiuc.lib.siu.edu/theses/1989.

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A Latin square of order n is an n × n array in which each row and column contains symbols from an n-set, S = {a1,...,an}, exactly once. If two Latin squares L1 and L2 of the same order can be joined such that each of the n^2 ordered pairs (ai,aj) appears exactly once, then L1 and L2 are said to be orthogonal. This project will involve a variation of this idea. We define orthogonality of two Latin squares Lm and Ln, for m < n, as follows: When we place an m × m Latin square Lm inside an n × n Latin square Ln, in all possible ways, the so obtained m^2 ordered pairs (ai,aj) are always distinct. We
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13

Chigbu, Polycarp Emeka. "Semi-Latin squares : methods for enumeration and comparison." Thesis, Goldsmiths College (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.363083.

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14

Henderson, Matthew James. "Embedding Symmetric Latin Squares and Edge-Coloured graphs." Thesis, University of Reading, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485356.

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In this thesis the closely related problems of embedding symmetric latin rectangles and embedding properly edge-coloured complete graphs are considered. The thesis is divided into three parts. The first part is an introductio~ and survey about completing partial latin squares and embedding latin rectangles. The second part is a proof of a former conjecture of Dugdale and Hilton about embedding edge-coloured complete graphs and the third and final part is a partial generalisation of the second part to the problem of embedding symmetric latin squares.
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15

Mourtos, Ioannis. "Integer and Constraint programming methods for mutually Orthogonal Latin Squares." Thesis, London School of Economics and Political Science (University of London), 2003. http://etheses.lse.ac.uk/2515/.

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This thesis examines the Orthogonal Latin Squares (OLS) problem from the viewpoint of Integer and Constraint programming. An Integer Programming (IP) model is proposed and the associated polytope is analysed. We identify several families of strong valid inequalities, namely inequalities arising from cliques, odd holes, antiwebs and wheels of the associated intersection graph. The dimension of the OLS polytope is established and it is proved that certain valid inequalities are facet-inducing. This analysis reveals also a new family of facet-defining inequalities for the polytope associated with
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16

Olsson, Christoffer. "Discreet Discrete Mathematics : Secret Communication Using Latin Squares and Quasigroups." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-136860.

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This thesis describes methods of secret communication based on latin squares and their close relative, quasigroups. Different types of cryptosystems are described, including ciphers, public-key cryptosystems, and cryptographic hash functions. There is also a chapter devoted to different secret sharing schemes based on latin squares. The primary objective is to present previously described cryptosystems and secret sharing schemes in a more accessible manner, but this text also defines two new ciphers based on isotopic latin squares and reconstructs a lost proof related to row-latin squares.<br>
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17

Burgess, D. R. B. "Uniquely completable and critical sets for graph colourings and Latin squares." Thesis, University of Surrey, 1998. http://epubs.surrey.ac.uk/842906/.

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It is possible for certain combinatorial structures to be uniquely defined with only partial information. The amount of information may be reduced until each part is critical for reconstruction. This thesis examines such 'uniquely completable' and 'critical sets' for 'Latin squares' and 'graph colourings', focusing on small and minimal critical sets. We aim to contribute to the current knowledge but also to illustrate why this knowledge is limited. We present critical sets of small cardinal in one of a certain family of Latin squares and prove that for a vast range of Latin squares there is at
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18

Carter, James Michael. "Mutually orthogonal latin squares based on ℤ3× ℤ9". Wright State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=wright1186687248.

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19

Baker, Charla Lindner Charles C. "The intersection problem for Latin squares with holes of size 2 and 3." Auburn, Ala, 2009. http://hdl.handle.net/10415/1670.

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20

Göransson, Herman. "Completing partial latin squares with 2 filled rows and 3 filled columns." Thesis, Linköpings universitet, Matematiska institutionen, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-163092.

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The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b completed columns and all other cells empty. We identify reductions of partial latin squares in PLS(2, 3; n) by using permutations described by filled rows and intersections of filled rows and columns. We find that all partial latin squares in PLS(2, 3;n), where n is sufficiently large, can be completed if such a reduction can be completed. We also show that all partial latin squares in PLS(2, 3; n) where the intersection of filled rows and columns form a latin rectangle have completions for n ≥ 8.
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21

Benade, Johannes Gerhardus. "A distributed system for enumerating main classes of sets of orthogonal Latin squares." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/96087.

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Thesis (MSc)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: A Latin square is an n n array containing n copies of each of n distinct symbols in such a way that no symbol is repeated in any row or column. Two Latin squares are orthogonal if, when superimposed, the ordered pairs in the n2 cells are all distinct. This notion of orthogonality extends naturally to sets of k > 2 mutually orthogonal Latin squares (abbreviated in the literature as k-MOLS), which nd application in scheduling problems and coding theory. In these instances it is important to di erentiate between structurally
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22

Farias, Fausto Gustavo. "Quadrados latinos e quadrados mágicos - uma proposta didática." Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9463.

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Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-08T12:22:35Z No. of bitstreams: 1 QUADRADOS LATINOS E QUADRADOS MÁGICOS UMA PROPOSTA DIDÁTICA.pdf: 24072473 bytes, checksum: 1d47842f904bd89accec69224c2a3c26 (MD5)<br>Approved for entry into archive by Fernando Souza (fernandoafsou@gmail.com) on 2017-09-08T13:27:24Z (GMT) No. of bitstreams: 1 QUADRADOS LATINOS E QUADRADOS MÁGICOS UMA PROPOSTA DIDÁTICA.pdf: 24072473 bytes, checksum: 1d47842f904bd89accec69224c2a3c26 (MD5)<br>Made available in DSpace on 2017-09-08T13:27:24Z (GMT). No. of bitstreams: 1 QUADRADOS LATINO
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23

Bobga, Benkam Benedict Johnson Peter D. "Some necessary conditions for list colorability of graphs and a conjecture on completing partial Latin squares." Auburn, Ala, 2008. http://repo.lib.auburn.edu/EtdRoot/2008/FALL/Mathematics_and_Statistics/Dissertation/Bobga_Benkam_22.pdf.

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24

Kidd, Martin Philip. "On the existence and enumeration of sets of two or three mutually orthogonal Latin squares with application to sports tournament scheduling." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/20038.

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Thesis (PdD)--Stellenbosch University, 2012.<br>ENGLISH ABSTRACT: A Latin square of order n is an n×n array containing an arrangement of n distinct symbols with the property that every row and every column of the array contains each symbol exactly once. It is well known that Latin squares may be used for the purpose of constructing designs which require a balanced arrangement of a set of elements subject to a number of strict constraints. An important application of Latin squares arises in the scheduling of various types of balanced sports tournaments, the simplest example of which is a
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25

Bedford, David. "Finite left neofields and their use as a unifying principle in constructions for orthogonal Latin squares." Thesis, University of Surrey, 1991. http://epubs.surrey.ac.uk/843470/.

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One of the outstanding problems in the study of Latin squares is that of improving the known lower bounds for N(n), the maximum number of Latin squares of order n in a mutually orthogonal set. After describing the methods of construction which attain the best known lower bounds for N(n), n < 32 and showing how most of these are interrelated we provide a general method of construction for sets of mutually orthogonal Latin squares (m.o.l.s.) from left neofields. We then give detailed information about the structure of all isomorphically distinct left neofields of order less than ten and about th
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26

Öhman, Lars-Daniel. "How to do what you want to do when you can not do what you want : on avoiding and completing partial latin squares." Doctoral thesis, Umeå University, Mathematics and Mathematical Statistics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-867.

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27

Mariot, Luca. "Automates cellulaires, fonctions booléennes et dessins combinatoires." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4011/document.

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Le but de cette thèse est l'étude des Automates Cellulaires (AC) dans la perspective des fonctions booléennes et des dessins combinatoires. Au-delà de son intérêt théorique, cette recherche est motivée par ses applications à la cryptographie, puisque les fonctions booléennes et les dessins combinatoires sont utilisés pour construire des générateurs de nombres pseudo aléatoires (Pseudorandom Number Generators, PRNG) et des schémas de partage de secret (Secret Sharing Schemes, SSS). Les résultats présentés dans la thèse ont été développés sur trois lignes de recherche, organisées comme suit. La
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28

Öhman, Lars-Daniel. "How to do what you want to do when you can not do what you want : on avoiding and completing partial latin squares /." Umeå : Department of Mathematics and Mathematical Statistics, Umeå University, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-867.

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29

Sanches, Paula da Fonte. "Quadrados latinos balanceados para a vizinhança - planejamento e análise de dados sensoriais por meio da ADQ." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-25022010-090439/.

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As avaliações sensoriais tomam cada vez mais sua posição de importância dentro dos centros produtores e vendedores de alimentos e de outros produtos. Nestes, o objetivo final dos trabalhos realizados nas áreas de desenvolvimento, produção e `marketing\' e o consumidor, cuja avaliação se baseia, principalmente, na aceitabilidade e custos dos produtos. Nesses experimentos, uma serie de tratamentos e dada para cada provador, e um problema relevante e que a variável resposta dependa não só do tratamento aplicado atualmente, mas também do anterior seguido a ele, chamados de efeitos residuais. Visan
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30

Gunturkun, Mustafa Hakan. "Using Tropical Degenerations For Proving The Nonexistence Of Certain Nets." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612076/index.pdf.

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A net is a special configuration of lines and points in the projective plane. There are certain restrictions on the number of its lines and points. We proved that there cannot be any (4,4) nets in CP^2. In order to show this, we use tropical algebraic geometry. We tropicalize the hypothetical net and show that there cannot be such a configuration in CP^2.
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31

Gongora-Aldaz, José Antonio. "On the addition of further treatments to Latin Square designs." Thesis, University of Warwick, 1997. http://wrap.warwick.ac.uk/73127/.

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Statisticians have made use of Latin Squares for randomized trials in the design of comparative experiments since the 1920s. Through cross-disciplinary use of Group theory, Statistics and Computing Science the author looks at the applications of the Latin Square as row-column design for scientific comparative experiments. The writer presents his argument, based on likelihood theory, for an F-test on Latin Square designs. A distinction between the combinatorial object and the row-column design known as the Latin Square is explicitly presented for the first time. Using statistical properties tog
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32

Santos, Ricardo Pessoa dos. "A matemática por trás do sudoku, um estudo de caso em análise combinatória." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/152320.

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Flores, Nichole Marie. "Guadalupe in the Public Square: Religious Aesthetics and the Pursuit of Justice." Thesis, Boston College, 2015. http://hdl.handle.net/2345/bc-ir:104548.

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Thesis advisor: Lisa Cahill<br>This dissertation investigates the relationship between religious aesthetics and justice in the pursuit of the societal common good. The orienting problem of the work is the tensive relationship between maintaining political stability and meaningful engagement with religious particularity in order to foster robust democratic participation, especially among communities that have been historically marginalized in American public life. This project interrogates the relationship between religion in public life through the specific locus of religious aesthetics: what
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34

Walker, DayVon L. "Power Graphs of Quasigroups." Scholar Commons, 2019. https://scholarcommons.usf.edu/etd/7984.

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We investigate power graphs of quasigroups. The power graph of a quasigroup takes the elements of the quasigroup as its vertices, and there is an edge from one element to a second distinct element when the second is a left power of the first. We first compute the power graphs of small quasigroups (up to four elements). Next we describe quasigroups whose power graphs are directed paths, directed cycles, in-stars, out-stars, and empty. We do so by specifying partial Cayley tables, which cannot always be completed in small examples. We then consider sinks in the power graph of a quasigroup,
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35

Steen, Ian Nicholas. "Application of a Latin square experimental design in health services research : estimation of the effects of setting clinical standards and performance review on the process and outcome of care in general practice." Thesis, University of Newcastle Upon Tyne, 1998. http://hdl.handle.net/10443/627.

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The North of England Study of Standards and Performance in General Practice was set up to investigate whether the setting of clinical standards was an effective way of improving clinical performance (North of England Study, 1991). Doctors from 60 training practices met in small groups to set standards of good clinical performance for five symptomatic conditions of childhood-acute cough; acute vomiting; itchy rash; bedwetting; and recurrent wheezy chest. Data on the process and outcome of care were collected both before and after standard setting process. Some of the baseline data was fed back
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36

Casselgren, Carl Johan. "On some graph coloring problems." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-43389.

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37

Ali, Mohamad Jaafar. "Wireless body area networks : co-channel interference mitigation & avoidance." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCB252/document.

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L’amélioration de la qualité et de l’efficacité en santé est un réel enjeu sociétal. Elle implique la surveillance continue des paramètres vitaux ou de l’état mental du sujet. Les champs d’applications sont vastes : l’application la plus importante est la surveillance des patients à distance. Les avancées en micro-électronique, capteurs et réseaux sans-fil permettent aujourd’hui le développement de systèmes ambulatoires performants pour le monitoring de paramètres physiologiques, capables de prendre en compte d’importantes contraintes techniques : forte intégration pour la réduction de la tail
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Ali, Mohamad Jaafar. "Wireless body area networks : co-channel interference mitigation & avoidance." Electronic Thesis or Diss., Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCB252.

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L’amélioration de la qualité et de l’efficacité en santé est un réel enjeu sociétal. Elle implique la surveillance continue des paramètres vitaux ou de l’état mental du sujet. Les champs d’applications sont vastes : l’application la plus importante est la surveillance des patients à distance. Les avancées en micro-électronique, capteurs et réseaux sans-fil permettent aujourd’hui le développement de systèmes ambulatoires performants pour le monitoring de paramètres physiologiques, capables de prendre en compte d’importantes contraintes techniques : forte intégration pour la réduction de la tail
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39

Lebon, Jérémy. "Towards multifidelity uncertainty quantification for multiobjective structural design." Phd thesis, Université de Technologie de Compiègne, 2013. http://tel.archives-ouvertes.fr/tel-01002392.

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This thesis aims at Multi-Objective Optimization under Uncertainty in structural design. We investigate Polynomial Chaos Expansion (PCE) surrogates which require extensive training sets. We then face two issues: high computational costs of an individual Finite Element simulation and its limited precision. From numerical point of view and in order to limit the computational expense of the PCE construction we particularly focus on sparse PCE schemes. We also develop a custom Latin Hypercube Sampling scheme taking into account the finite precision of the simulation. From the modeling point of vie
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40

Chan, Cheng-I., and 陳靜儀. "Transversals in Latin Squares." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/6ey4af.

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碩士<br>國立交通大學<br>應用數學系所<br>106<br>A Latin square of order n based on an n-set S is an n x n array L such that each element of S occurs in each row and each column of L exactly once. A transversal T of L is a set of n entries one from each column and each row. The number of distinct entries in T is denoted by t_n. If t_n=n, then T is known as a Latin transversal of L. Given a Latin square of order n, L, it is interesting to know the maximum size of $t_n$ where T is a transversal. Of course, we may list all n! transversals to find the answer. But, if n is getting larger, it is getting more compl
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41

Liu, Shu-Hui, and 劉曙輝. "New algorithms for N Latin squares." Thesis, 1988. http://ndltd.ncl.edu.tw/handle/13742039993171870432.

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42

GUO, SAN-HUI, and 郭三輝. "The intersections of commutative Latin squares." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/86808743995258455663.

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43

Li, Jung Feng, and 李榮蘴. "Critical sets of special latin squares." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/46269856670257644780.

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碩士<br>淡江大學<br>數學學系<br>86<br>A latin square L of order n is an nxn array with entries in N ={1,2,...,n}such that each element of N occurs precisely once in each row and each column of the array. A latin square Ｌ=〔ｌ 〕is said to be commutative if ｌ =ｌ ij ij ji for each i,j=1,2,..., n. A latin square is said to be an idempotent if ｌ =ｉ　 ii for each i=1,2,...,n. A partial latin square P, of order n, is an nxn array with some cells contai
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44

YU, JYUN-REN, and 俞竣仁. "Decoder Implementation of Latin Squares LDPC Codes." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/89454749112570694794.

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碩士<br>國立臺灣科技大學<br>電機工程系<br>101<br>With the advance of new IC technology, more bits of data can be stored in each flash memory cell to increase capacity of storage; however, it reduces the reliability of flash memory cell. In tradition, BCH code is commonly used in NAND flash memory. BCH can only increase parity bits to correct large number of errors such that storage capacity is reduced. Hence, it is necessary to find a new error correcting code with higher rate and error correcting capability. To solve this problem, LDPC code is a good candidate. When soft information is used to decode stored
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45

Shen, Yuh-Ying, and 沈煜瑩. "r-orthogonal latin squares of order n." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/94983196600878076175.

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碩士<br>淡江大學<br>數學系<br>83<br>A latin square L of order n is a nxn matrix whose entries are elements of a set S of n symbols and which has the property that each symbol occurs exactly once in each row and exactly once in each column of L. Two latin squares of order n are called orthogonal if, when they are superimposed, exactly nxn different ordered pairs occur among the nxn ordered pairs of cells .Two latin squares of order n are called r-orthogonal if, when they are superimposed, exactly r
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46

Bartlett, Padraic James. "Completions of ε-Dense Partial Latin Squares". Thesis, 2013. https://thesis.library.caltech.edu/7819/1/caltech_dissertation_padraic_draft.pdf.

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<p>A classical question in combinatorics is the following: given a partial Latin square $P$, when can we complete $P$ to a Latin square $L$? In this paper, we investigate the class of textbf{$epsilon$-dense partial Latin squares}: partial Latin squares in which each symbol, row, and column contains no more than $epsilon n$-many nonblank cells. Based on a conjecture of Nash-Williams, Daykin and H"aggkvist conjectured that all $frac{1}{4}$-dense partial Latin squares are completable. In this paper, we will discuss the proof methods and results used in previous attempts to resolve this conjec
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47

Tsai, Shu-Hui, and 蔡淑慧. "Orthogonality of Latin squares defined by abelian groups." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/9e9b5v.

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碩士<br>國立中山大學<br>應用數學系研究所<br>96<br>Let G = {g1, …,gn} be a finite abelian group, and let LG = [gij ] be the Latin square defined by gij = gi + gj. Denote by k(G) the largest number of mutually orthogonal system containing LG. In 1948, Paige showed that if the Sylow 2-subgroup of G is not cyclic, then LG has a transversal. In this paper, we give an constructive proof for this theorem and give some upper bound and lower bound for the number k(G).
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48

Howell, Jared. "Intersection problem and different pairs problem for Latin squares." Thesis, 2010. http://hdl.handle.net/1828/3095.

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The intersection of two Latin squares of the same order is the set of cells that contain the same entries in both Latin squares. Determining the order of this set can be asked for any type of Latin square and has been solved for most. Generalizing this to Latin squares of different orders leads to a conjecture of Dukes and Mendelsohn, which will be shown to be true. Results on the intersection of Latin squares, idempotent Latin squares, and idempotent symmetric Latin squares are explored. The relationship between the intersection problem for Latin squares and the intersection problem for Stein
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Chen, Hsin-yu, and 陳欣妤. "High Effciency Decoder Implementation of Latin Squares LDPC Codes." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/60138536563924570522.

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碩士<br>國立臺灣科技大學<br>電機工程系<br>102<br>This thesis realizes the hardware architecture of the LDPC decoder, where the (9241,8240) LDPC code is constructed based on the Latin Square with code rate 0.89. The variable-node-centric sequential scheduling (VSS) technology is adopted to reduce hardware complexity and utilization efficiently. In contrast to the traditional Min-Sum decoder, the proposed VSS technology not only reduces the iteration times, but also hardware implementation cost and complexity of routing network. By using TSMC180nm CMOS technology to implement decoder, the maximum throughput ca
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50

van, Bommel Christopher Martin. "An Asymptotic Existence Theory on Incomplete Mutually Orthogonal Latin Squares." Thesis, 2015. http://hdl.handle.net/1828/5930.

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An incomplete Latin square is a v x v array with an empty n x n subarray with every row and every column containing each symbol at most once and no row or column with an empty cell containing one of the last n symbols. A set of t incomplete mutually orthogonal Latin squares of order v and hole size n is a set of t incomplete Latin squares (containing the same empty subarray on the same set of symbols) with a natural extension to the condition of orthogonality. The existence of such sets have been previously explored only for small values of t. We determine an asymptotic result for the existe
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