Relevant bibliographies by topics / Catalan Numbers

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Catalan Numbers'

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

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Journal articles on the topic "Catalan Numbers"

1

Ardila, Federico. "Catalan Numbers." Mathematical Intelligencer 38, no. 2 (2016): 4–5. http://dx.doi.org/10.1007/s00283-016-9625-6.

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Andrews, George E. "Catalan numbers, q-Catalan numbers and hypergeometric series." Journal of Combinatorial Theory, Series A 44, no. 2 (1987): 267–73. http://dx.doi.org/10.1016/0097-3165(87)90033-1.

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He, Tian-Xiao. "Parametric Catalan numbers and Catalan triangles." Linear Algebra and its Applications 438, no. 3 (2013): 1467–84. http://dx.doi.org/10.1016/j.laa.2012.10.001.

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Berenstein, Arkady, and Vladimir Retakh. "Noncommutative Catalan Numbers." Annals of Combinatorics 23, no. 3-4 (2019): 527–47. http://dx.doi.org/10.1007/s00026-019-00473-4.

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Fürlinger, J., and J. Hofbauer. "q-Catalan numbers." Journal of Combinatorial Theory, Series A 40, no. 2 (1985): 248–64. http://dx.doi.org/10.1016/0097-3165(85)90089-5.

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Rubenstein, Daniel. "Catalan numbers revisited." Journal of Combinatorial Theory, Series A 68, no. 2 (1994): 486–90. http://dx.doi.org/10.1016/0097-3165(94)90119-8.

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Olive, Gloria. "Catalan numbers revisited." Journal of Mathematical Analysis and Applications 111, no. 1 (1985): 201–35. http://dx.doi.org/10.1016/0022-247x(85)90212-4.

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Hein, Nickolas, and Jia Huang. "Modular Catalan numbers." European Journal of Combinatorics 61 (March 2017): 197–218. http://dx.doi.org/10.1016/j.ejc.2016.11.004.

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Galashin, Pavel, and Thomas Lam. "Positroid Catalan numbers." Communications of the American Mathematical Society 4, no. 8 (2024): 357–86. http://dx.doi.org/10.1090/cams/33.

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Given a (bounded affine) permutation f f , we study the positroid Catalan number C f C_f defined to be the torus-equivariant Euler characteristic of the associated open positroid variety. We introduce a class of repetition-free permutations and show that the corresponding positroid Catalan numbers count Dyck paths avoiding a convex subset of the rectangle. We show that any convex subset appears in this way. Conjecturally, the associated q , t q,t -polynomials coincide with the generalized q , t q,t -Catalan numbers that recently appeared in relation to the shuffle conjecture, flag Hilbert sche
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Krystek, Anna Dorota, and Łukasz Jan Wojakowski. "Remarks on Catalan and super-Catalan numbers." Banach Center Publications 96 (2011): 237–44. http://dx.doi.org/10.4064/bc96-0-15.

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Dissertations / Theses on the topic "Catalan Numbers"

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An, Junkyu. "Combinatorial enumeration of weighted Catalan numbers." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/64609.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 69-70).<br>This thesis is devoted to the divisibility property of weighted Catalan and Motzkin numbers and its applications. In Chapter 1, the definitions and properties of weighted Catalan and Motzkin numbers are introduced. Chapter 2 studies Wilf conjecture on the complementary Bell number, the alternating sum of the Stirling number of the second kind. Congruence properties of the complementary Bell numbers are found by weight
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Richardson, Steven L. "Enumeration of the generalized Catalan numbers." Morgantown, W. Va. : [West Virginia University Libraries], 2005. https://etd.wvu.edu/etd/controller.jsp?moduleName=documentdata&jsp%5FetdId=3906.

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Allen, Emily. "Combinatorial Interpretations Of Generalizations Of Catalan Numbers And Ballot Numbers." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/366.

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The super Catalan numbers T(m,n) = (2m)!(2n)!=2m!n!(m+n)! are integers which generalize the Catalan numbers. Since 1874, when Eugene Catalan discovered these numbers, many mathematicians have tried to find their combinatorial interpretation. This dissertation is dedicated to this open problem. In Chapter 1 we review known results on T (m,n) and their q-analog polynomials. In Chapter 2 we give a weighted interpretation for T(m,n) in terms of 2-Motzkin paths of length m+n2 and a reformulation of this interpretation in terms of Dyck paths. We then convert our weighted interpretation into a conven
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Mott, Brittany Nicole. "Analysis of the Generalized Catalan Orbits." University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750.

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Guerrini, Veronica. "On enumeration sequences generalising Catalan and Baxter numbers." Doctoral thesis, Università di Siena, 2018. http://hdl.handle.net/11365/1035968.

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The study carried out along this dissertation fits into the field of enumerative combinatorics. The structures that have been investigated are families of discrete objects which display combinatorial properties. They are mainly subfamilies of well-known combinatorial structures, such as lattice paths, pattern-avoiding permutations, polyominoes (more specifically, parallelogram polyominoes), or inversion sequences. Furthermore, these combinatorial families are closely related to two famous number sequences known in the literature as the Catalan and Baxter numbers. We start defining and s
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Auger, Joseph Thomas. "Orbits of the Dissected Polygons of the Generalized Catalan Numbers." University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302701692.

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Loehr, Nicholas Anthony. "Multivariate analogues of Catalan numbers, parking functions, and their extensions /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2003. http://wwwlib.umi.com/cr/ucsd/fullcit?p3091333.

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Brasil, Junior Nelson Gomes 1989. "Bijeções envolvendo os números de Catalan." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307511.

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Orientador: José Plínio de Oliveira Santos<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-25T04:32:08Z (GMT). No. of bitstreams: 1 BrasilJunior_NelsonGomes_M.pdf: 980636 bytes, checksum: dd8d61baeb633d5f598abc3523def800 (MD5) Previous issue date: 2014<br>Resumo: Neste trabalho, estudamos a sequência dos Números de Catalan, uma sequência que aparece como solução de vários problemas de contagem envolvendo árvores, palavras, grafos e outras estruturas combinatórias. Atualmente, são
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Drescher, Chelsea. "Invariants of Polynomials Modulo Frobenius Powers." Thesis, University of North Texas, 2020. https://digital.library.unt.edu/ark:/67531/metadc1703327/.

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Rational Catalan combinatorics connects various Catalan numbers to the representation theory of rational Cherednik algebras for Coxeter and complex reflection groups. Lewis, Reiner, and Stanton seek a theory of rational Catalan combinatorics for the general linear group over a finite field. The finite general linear group is a modular reflection group that behaves like a finite Coxeter group. They conjecture a Hilbert series for a space of invariants under the action of this group using (q,t)-binomial coefficients. They consider the finite general linear group acting on the quotient of a pol
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Valqui, Haase Christian Holger, and Marco Solórzano. "The Groebner basis of a polynomial system related to the Jacobian conjecture." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95235.

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We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers.<br>En este artículo calculamos la base de Groebner de un sistema polinomial de ecuaciones relacionada con la conjetura del jacobiano utilizando una fórmula recursiva para los numeros de Catalan.
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Books on the topic "Catalan Numbers"

1

Roman, Steven. An Introduction to Catalan Numbers. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22144-1.

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Grimaldi, Ralph P. Fibonacci and catalan numbers: An introduction. John Wiley & Sons, 2012.

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Haglund, James. The q, t-Catalan numbers and the space of diagonal harmonics: With an appendix on the combinatorics of Macdonald polynomials. American Mathematical Society, 2008.

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Schoof, René. Catalan's conjecture. Springer, 2008.

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Otroshko, Sergey, Alexey Shevtsov, Vladimir Kosolapov, and Nelly Georgiadi. The Patents of the Federal Scientific Center "VIK named after V. R. Williams" 2000–2024. Federal Williams Research Center of Forage Production and Agroecology, 2024. http://dx.doi.org/10.33814/catalog-2024-80.

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The catalog contains descriptions of patents of the Federal Scientific Center “VIK im. In R. Williams" on inventions and utility models for the period 2000–2024. in the field of mechanization, canning and storage of feed, field and meadow feed production, selection and seed production processes, procurement and storage of high-quality bulk feed, grass meal, feed sampling, and manure disposal. Each publication about a patent for an invention (utility model) contains the name of the invention (utility model), International Patent Classification (IPC) indices, patent number, application number, p
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United States. National Archives and Records Administration. and Church of Jesus Christ of Latter-Day Saints. Genealogical Library., eds. A Key to the 1880 United States federal census identifying enumeration district numbers and microfilm numbers of the National Archives and the Genealogical Library. 2nd ed. Heritage Books, 1986.

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Busacca, Maurizio, and Roberto Paladini. Collaboration Age. Fondazione Università Ca’ Foscari, 2020. http://dx.doi.org/10.30687/978-88-6969-424-0.

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Recently, public policies of urban regeneration have intensified and multiplied. They are being promoted with the aim to start social and economic dynamics within the local context which is subject to intervention. From the empirical analysis, we realise that such activities are mainly implemented by three subjects or by mixed coalitions (public institutions, actors of the third sector and companies). Within them, each player is moved by a multiplicity of interests and goals that go beyond their own nature – public interest, market and mutualism – and tend to redefine themselves, thus becoming
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Koshy, Thomas. Catalan Numbers with Applications. Oxford University Press, 2009.

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Koshy, Thomas. Catalan Numbers with Applications. Oxford University Press, Incorporated, 2009.

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Stanley, Richard P. Catalan Numbers. Cambridge University Press, 2015.

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Book chapters on the topic "Catalan Numbers"

1

Hilton, Peter, Derek Holton, and Jean Pedersen. "Catalan Numbers." In Undergraduate Texts in Mathematics. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-3681-6_7.

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Moll, Victor. "Catalan numbers." In The Student Mathematical Library. American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/065/06.

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Roman, Steven. "The Catalan Numbers." In Compact Textbooks in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22144-1_3.

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Berenstein, Arkady, and Vladimir Retakh. "Noncommutative Catalan Numbers." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-57050-7_10.

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Petersen, T. Kyle. "Catalan and Narayana numbers." In Inquiry-Based Enumerative Combinatorics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18308-0_9.

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Roman, Steven. "Catalan Numbers and Permutations." In Compact Textbooks in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22144-1_10.

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Roman, Steven. "Catalan Numbers and Semiorders." In Compact Textbooks in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22144-1_11.

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Roman, Steven. "Catalan Numbers and Paths." In Compact Textbooks in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22144-1_4.

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Roman, Steven. "Catalan Numbers and Trees." In Compact Textbooks in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22144-1_5.

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Roman, Steven. "Catalan Numbers and Partitions." In Compact Textbooks in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22144-1_9.

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Conference papers on the topic "Catalan Numbers"

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Aroukatos, Nikolaos, Kostas Manes, Stelios Zimeras, and Fotis Georgiakodis. "Data Hiding Techniques in Steganography Using Fibonacci and Catalan Numbers." In 2012 Ninth International Conference on Information Technology: New Generations (ITNG). IEEE, 2012. http://dx.doi.org/10.1109/itng.2012.96.

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Pengelley, David, Inna Pivkina, Desh Ranjan, and Karen Villaverde. "A project in algorithms based on a primary historical source about catalan numbers." In the 37th SIGCSE technical symposium. ACM Press, 2006. http://dx.doi.org/10.1145/1121341.1121439.

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Gasparyan, Armenak Sokratovich. "Combinatorial identities over recurrent sequences." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-45.

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The article presents several general identities, special cases which are many well-known identities such as, for example, Cassini, Catalan, Taguiri identities for Fibonacci numbers, their analogues and generalizations to other Fibonacci-type numbers.
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Mikić, Jovan. "On divisibility properties of some binomial sums connected with the Catalan and Fibonacci numbers." In 4th Croatian Combinatorial Days. University of Zagreb Faculty of Civil Engineering, 2023. http://dx.doi.org/10.5592/co/ccd.2022.05.

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Varga, Daria, Lana Dujmović, Isidora Đurić, Lidija Krstanović, Danijela Milekić, and Ana Perišić. "BASIC COMPUTATIONAL GEOMETRY APPLICATIONS IN COMPUTER GRAPHICS." In The 9th Conference on Mathematics in Engineering: Theory and Applications. Faculty of Technical Sciences, University of Novi Sad, 2024. http://dx.doi.org/10.24867/meta.2024.26.

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This paper explores fundamental applications of computational geometry in computer graphics. It demonstrates the implementation and visualization of examples including the art gallery problem, utilizing Catalan numbers, as well as applications of 2D and 3D convex hulls. The demonstrations are carried out using the Python programming language in conjunction with Blender 3D modeling software. The paper illustrates the broad utility of computational geometry concepts in computer graphics, such as automatically extracting parts of 2D images or calculating convex hulls for various types of 3D objec
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López García, Esmeralda. "La mediterraneidad en la obra de Le Corbusier. La bóveda catalana lecorbuseriana: Influencias y evolución." In LC2015 - Le Corbusier, 50 years later. Universitat Politècnica València, 2015. http://dx.doi.org/10.4995/lc2015.2015.527.

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Resumen: Le Corbusier durante gran parte de su vida busca volver la vista hacia las tradiciones mediterráneas. Con el fin de desvelar la arquitectura y el paisaje españoles, realiza un gran número de viajes en tren y coche a lo largo de su territorio y será durante su visita a Barcelona en 1928 cuando nace su interés por la técnica de la bóveda catalana. Es una época de su carrera en la que empieza a interesarse por métodos de construcción y materiales tradicionales. Para el arquitecto la bóveda catalana es un sistema con grandes posibilidades formales y una gran flexibilidad frente a su senci
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"IEEE Catalog Number: 06EX1626." In 2006 Optics Valley of China International Symposium on Optoelectronics. IEEE, 2006. http://dx.doi.org/10.1109/ovciso.2006.302715.

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"IEEE Catalog Number: 06EX1439." In 2006 IEEE/ASME International Conference on Mechatronics and Embedded Systems and Applications. IEEE, 2006. http://dx.doi.org/10.1109/mesa.2006.296923.

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Kianfar, Kamran, Mehdi Fathi, Amir Hasanzadeh, and Amir Sadeghi. "Catalog segmentation with the objective of satisfying customer requirements in minimum number of catalog." In 2009 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM). IEEE, 2009. http://dx.doi.org/10.1109/ieem.2009.5373003.

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"IEEE Catalog Number: 04EX907 / ISBN: 0-7803-8631-0 [Back Cover]." In 2nd Workshop onEmbedded Systems for Real-Time Multimedia, 2004. ESTImedia 2004. IEEE, 2004. http://dx.doi.org/10.1109/estmed.2004.1359720.

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Reports on the topic "Catalan Numbers"

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Weinstein, Emily. Chinese Talent Program Tracker. Center for Security and Emerging Technology, 2020. http://dx.doi.org/10.51593/20200066.

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China operates a number of party- and state-sponsored talent programs to recruit researchers -- Chinese citizens and non-citizens alike -- to bolster its strategic civilian and military goals. CSET has created a tracker to catalog publicly available information about these programs. This catalog is a work in progress; if you have further information on programs currently not included in it -- or if you spot an error -- please complete the form at http://bit.ly/ChineseTalent
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Quinn, Cathy A., Philip K. Hamilton, Scott D. Kraus, and Christopher K. Slay. An assessment of wounds caused by the attachment of remote sensing tags to North Atlantic right whales (Eubalaena Glacialis): 1988 - 1997. New England Aquarium and Woods Hole Oceanographic Institution, 2023. http://dx.doi.org/10.1575/1912/29702.

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Because of the increase in usage of remote sensing tags to track the migration and movements of cetaceans, it has become increasingly important to assess the impact of such techniques on the target species. Between 1988 and 1997, 55 tags (41 satellite telemetry, 14 VHF or acoustic radio transmitter) were attached to 49 North Atlantic right whales (Eubalaena glacialis). All tags had implantable barbs or were fully implanted below the dermis. Right whales are photographically identifiable and the New England Aquarium curates the North Atlantic catalog, which currently numbers 374 individuals. Th
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Miley, S. J. Addendum to a catalog of low Reynolds number airfoil data for wind turbine applications. Office of Scientific and Technical Information (OSTI), 1985. http://dx.doi.org/10.2172/5801393.

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Pecor, James E., Varuni L. Mallampalli, Ralph E. Harbach, and E. L. Peyton. Contributions of the American Entomological Institute. Volume 27. Number 2. 1992. Catalog and Illustrated Review of the Subgenus Melanoconion of Culex (Diptera: Culicidae). Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada274863.

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Ko, Yura K., Wataru Kagaya, Mtakai Ngara, et al. Indirect effects of interventions for malaria: a scoping review protocol. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, 2023. http://dx.doi.org/10.37766/inplasy2023.6.0025.

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Review question / Objective: The aim of this review is to identify and catalog studies that have reported the impact of indirect effects in interventions targeting malaria. Specific review questions are the following. 1. How many studies explicitly reported indirect effects? a. Have the number of publications increased in recent years? 2. What methodologies were employed by these studies to estimate the indirect effects? 3. Which terminologies were used to describe indirect effects? Background: Malaria is still a major health problem, particularly in sub-Saharan Africa, where 98% of global mal
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Horwitz, Benjamin A., and Barbara Gillian Turgeon. Fungal Iron Acquisition, Oxidative Stress and Virulence in the Cochliobolus-maize Interaction. United States Department of Agriculture, 2012. http://dx.doi.org/10.32747/2012.7709885.bard.

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Our project focused on genes for high affinity iron acquisition in Cochliobolus heterostrophus, a necrotrophic pathogen of maize, and their intertwined relationship to oxidative stress status and virulence of the fungus on the host. An intriguing question was why mutants lacking the nonribosomal peptide synthetase (NRPS) gene (NPS6) responsible for synthesis of the extracellular siderophore, coprogen, are sensitive to oxidative stress. Our overall objective was to understand the mechanistic connection between iron stress and oxidative stress as related to virulence of a plant pathogen to its h
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Crowley, David E., Dror Minz, and Yitzhak Hadar. Shaping Plant Beneficial Rhizosphere Communities. United States Department of Agriculture, 2013. http://dx.doi.org/10.32747/2013.7594387.bard.

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PGPR bacteria include taxonomically diverse bacterial species that function for improving plant mineral nutrition, stress tolerance, and disease suppression. A number of PGPR are being developed and commercialized as soil and seed inoculants, but to date, their interactions with resident bacterial populations are still poorly understood, and-almost nothing is known about the effects of soil management practices on their population size and activities. To this end, the original objectives of this research project were: 1) To examine microbial community interactions with plant-growth-promoting r
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