Log in

Relevant bibliographies by topics / Lattice polytope

Contents

Journal articles
Dissertations / Theses
Books
Book chapters
Conference papers

Academic literature on the topic 'Lattice polytope'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Lattice polytope.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Lattice polytope"

1

HEGEDÜS, GÁBOR, and ALEXANDER M. KASPRZYK. "THE BOUNDARY VOLUME OF A LATTICE POLYTOPE." Bulletin of the Australian Mathematical Society 85, no. 1 (2011): 84–104. http://dx.doi.org/10.1017/s0004972711002577.

Full text

Abstract:

AbstractFor a d-dimensional convex lattice polytope P, a formula for the boundary volume vol(∂P) is derived in terms of the number of boundary lattice points on the first ⌊d/2⌋ dilations of P. As an application we give a necessary and sufficient condition for a polytope to be reflexive, and derive formulas for the f-vector of a smooth polytope in dimensions three, four, and five. We also give applications to reflexive order polytopes, and to the Birkhoff polytope.

APA, Harvard, Vancouver, ISO, and other styles

2

HILLE, LUTZ, та HARALD SKARKE. "REFLEXIVE POLYTOPES IN DIMENSION 2 AND CERTAIN RELATIONS IN SL2(ℤ)". Journal of Algebra and Its Applications 01, № 02 (2002): 159–73. http://dx.doi.org/10.1142/s0219498802000124.

Full text

Abstract:

It is well known that there are 16 two-dimensional reflexive polytopes up to lattice isomorphism. One can check directly from the list that the number of lattice points on the boundary of such a polytope plus the number of lattice points on the boundary of the dual polytope is always 12. It turns out that two-dimensional reflexive polytopes correspond to certain relations of two generators A and B of SL 2(ℤ) of length 12. We generalize this correspondence to reflexive configurations with winding number w and relations of length 12w.

APA, Harvard, Vancouver, ISO, and other styles

3

Ryshkov, S. S., and R. M. Erdahl. "The Empty Sphere Part II." Canadian Journal of Mathematics 40, no. 5 (1988): 1058–73. http://dx.doi.org/10.4153/cjm-1988-043-5.

Full text

Abstract:

Blow up a sphere in one of the interstices of a lattice until it is held rigidly. There will be no lattice points in the interior and sufficiently many on the boundary so that their convex hull is a solid figure. Such a sphere was called an empty sphere by B. N. Delone in 1924 when he introduced his method for lattice coverings [3, 4]. The circumscribed polytope is called an L-polytope. Our interest in such matters stems from the following result [6, Theorems 2.1 and 2.3]: With a list of the L-polytopes for lattices of dimension ≦n one can give a geometrical description of the possible sets of

APA, Harvard, Vancouver, ISO, and other styles

4

Koca, Mehmet, Nazife Ozdes Koca, Abeer Al-Siyabi, and Ramazan Koc. "Explicit construction of the Voronoi and Delaunay cells ofW(An) andW(Dn) lattices and their facets." Acta Crystallographica Section A Foundations and Advances 74, no. 5 (2018): 499–511. http://dx.doi.org/10.1107/s2053273318007842.

Full text

Abstract:

Voronoi and Delaunay (Delone) cells of the root and weight lattices of the Coxeter–Weyl groupsW(An) andW(Dn) are constructed. The face-centred cubic (f.c.c.) and body-centred cubic (b.c.c.) lattices are obtained in this context. Basic definitions are introduced such as parallelotope, fundamental simplex, contact polytope, root polytope, Voronoi cell, Delone cell,n-simplex,n-octahedron (cross polytope),n-cube andn-hemicube and their volumes are calculated. The Voronoi cell of the root lattice is constructed as the dual of the root polytope which turns out to be the union of Delone cells. It is

APA, Harvard, Vancouver, ISO, and other styles

5

Lalvani, Haresh. "Higher Dimensional Periodic Table Of Regular And Semi-Regular Polytopes." International Journal of Space Structures 11, no. 1-2 (1996): 155–71. http://dx.doi.org/10.1177/026635119601-222.

Full text

Abstract:

This paper presents a higher-dimensional periodic table of regular and semi-regular n-dimensional polytopes. For regular n-dimensional polytopes, designated by their Schlafli symbol {p,q,r,…u,v,w}, the table is an (n-1)-dimensional hypercubic lattice in which each polytope occupies a different vertex of the lattice. The values of p,q,r,…u,v,w also establish the corresponding n-dimensional Cartesian co-ordinates (p,q,r,…u,v,w) of their respective positions in the hypercubic lattice. The table is exhaustive and includes all known regular polytopes in Euclidean, spherical and hyperbolic spaces, i

APA, Harvard, Vancouver, ISO, and other styles

6

Dutour Sikirić, Mathieu. "The Seven Dimensional Perfect Delaunay Polytopes and Delaunay Simplices." Canadian Journal of Mathematics 69, no. 5 (2017): 1143–68. http://dx.doi.org/10.4153/cjm-2016-013-7.

Full text

Abstract:

AbstractFor a lattice L of ℝn, a sphere S(c, r) of center c and radius r is called empty if for any v ∈ L we have. Then the set S(c, r) ∩ L is the vertex set of a Delaunay polytope P = conv(S(c, r) ∩ L). A Delaunay polytope is called perfect if any aõne transformation ø such that ø(P) is a Delaunay polytope is necessarily an isometry of the space composed with an homothety.Perfect Delaunay polytopes are remarkable structures that exist only if n = 1 or n ≥ 6, and they have shown up recently in covering maxima studies. Here we give a general algorithm for their enumeration that relies on the Er

APA, Harvard, Vancouver, ISO, and other styles

7

Cho, Mi Ju, Jin Hong Kim, and Hwa Lee. "Criteria for Hattori–Masuda multi-polytopes via Duistermaat–Heckman functions and winding numbers." Advances in Geometry 18, no. 3 (2018): 355–72. http://dx.doi.org/10.1515/advgeom-2017-0023.

Full text

Abstract:

AbstractA multi-fan (respectively multi-polytope), introduced first by Hattori and Masuda, is a purely combinatorial object generalizing an ordinary fan (respectively polytope) in algebraic geometry. It is well known that an ordinary fan or polytope is associated with a toric variety. On the other hand, we can geometrically realize multi-fans in terms of torus manifolds. However, it is unfortunate that two different torus manifolds may correspond to the same multi-fan. The goal of this paper is to give some criteria for a multi-polytope to be an ordinary polytope in terms of the Duistermaat–He

APA, Harvard, Vancouver, ISO, and other styles

8

Bayer, Margaret, and Bernd Sturmfels. "Lawrence Polytopes." Canadian Journal of Mathematics 42, no. 1 (1990): 62–79. http://dx.doi.org/10.4153/cjm-1990-004-4.

Full text

Abstract:

In 1980 Jim Lawrence suggested a construction Λ which assigns to a given rank r oriented matroid M on n points a rank n + r oriented matroid Λ(M) on 2n points such that the face lattice of Λ(M) is polytopal if and only if M is realizable. The Λ-construction generalized a technique used by Perles to construct a nonrational polytope [10]. It was used by Lawrence to prove that the class of polytopal lattices is strictly contained in the class of face lattices of oriented matroids (unpublished) and by Billera and Munson to show that the latter class is not closed under polarity. See [4] for a disc

APA, Harvard, Vancouver, ISO, and other styles

9

Lagarias, Jeffrey C., and Günter M. Ziegler. "Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice." Canadian Journal of Mathematics 43, no. 5 (1991): 1022–35. http://dx.doi.org/10.4153/cjm-1991-058-4.

Full text

Abstract:

AbstractA lattice polytope is a polytope in whose vertices are all in . The volume of a lattice polytope P containing exactly k ≥ 1 points in d in its interior is bounded above by . Any lattice polytope in of volume V can after an integral unimodular transformation be contained in a lattice cube having side length at most n˙n ! V. Thus the number of equivalence classes under integer unimodular transformations of lattice poly topes of bounded volume is finite. If S is any simplex of maximum volume inside a closed bounded convex body K in having nonempty interior, then K⊆ ( n + 2)S — (n+ l)s whe

APA, Harvard, Vancouver, ISO, and other styles

10

Ardila, Federico, Matthias Beck, and Jodi McWhirter. "The arithmetic of Coxeter permutahedra." Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales 44, no. 173 (2020): 1152–66. http://dx.doi.org/10.18257/raccefyn.1189.

Full text

Abstract:

Ehrhart theory mesures a polytope P discretely by counting the lattice points inside its dilates P, 2P, 3P, ..... We compute the Ehrhart theory of four families of polytopes of great importance in several areas of mathematics: the standard Coxeter permutahedra for the classical Coxeter groups An, Bn, Cn, Dn. A central tool, of independent interest, is a description of the Ehrhart theory of a rational translate of an integer projection of a cube.

APA, Harvard, Vancouver, ISO, and other styles

More sources

Dissertations / Theses on the topic "Lattice polytope"

1

Hofmann, Jan [Verfasser]. "Three interesting lattice polytope problems / Jan Hofmann." Berlin : Freie Universität Berlin, 2018. http://d-nb.info/1153008092/34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Borger, Christopher Verfasser], and Benjamin [Gutachter] [Nill. "Mixed lattice polytope theory with a view towards sparse polynomial systems / Christopher Borger ; Gutachter: Benjamin Nill." Magdeburg : Universitätsbibliothek Otto-von-Guericke-Universität, 2020. http://d-nb.info/1220034908/34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Borger, Christopher [Verfasser], and Benjamin [Gutachter] Nill. "Mixed lattice polytope theory with a view towards sparse polynomial systems / Christopher Borger ; Gutachter: Benjamin Nill." Magdeburg : Universitätsbibliothek Otto-von-Guericke-Universität, 2020. http://nbn-resolving.de/urn:nbn:de:gbv:ma9:1-1981185920-347964.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Meyer, Marie. "Polytopes Associated to Graph Laplacians." UKnowledge, 2018. https://uknowledge.uky.edu/math_etds/54.

Full text

Abstract:

Graphs provide interesting ways to generate families of lattice polytopes. In particular, one can use matrices encoding the information of a finite graph to define vertices of a polytope. This dissertation initiates the study of the Laplacian simplex, PG, obtained from a finite graph G by taking the convex hull of the columns of the Laplacian matrix for G. The Laplacian simplex is extended through the use of a parallel construction with a finite digraph D to obtain the Laplacian polytope, PD. Basic properties of both families of simplices, PG and PD, are established using techniques from Ehrha

APA, Harvard, Vancouver, ISO, and other styles

5

Webb, Kerri. "Counting Bases." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1120.

Full text

Abstract:

A theorem of Edmonds characterizes when a pair of matroids has a common basis. Enumerating the common bases of a pair of matroid is a much harder problem, and includes the #P-complete problem of counting the number of perfect matchings in a bipartite graph. We focus on the problem of counting the common bases in pairs of regular matroids, and describe a class called <i>Pfaffian matroid pairs</i> for which this enumeration problem can be solved. We prove that when a pair of regular matroids is non-Pfaffian, there is a set of common bases which certifies this, and that the number of bases

APA, Harvard, Vancouver, ISO, and other styles

6

Gay, Joël. "Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS209/document.

Full text

Abstract:

La combinatoire algébrique est le champ de recherche qui utilise des méthodes combinatoires et des algorithmes pour étudier les problèmes algébriques, et applique ensuite des outils algébriques à ces problèmes combinatoires. L’un des thèmes centraux de la combinatoire algébrique est l’étude des permutations car elles peuvent être interprétées de bien des manières (en tant que bijections, matrices de permutations, mais aussi mots sur des entiers, ordre totaux sur des entiers, sommets du permutaèdre…). Cette riche diversité de perspectives conduit alors aux généralisations suivantes du groupe sy

APA, Harvard, Vancouver, ISO, and other styles

7

Lundman, Anders. "Classifying Lattice Polytopes." Licentiate thesis, KTH, Matematik (Avd.), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-134707.

Full text

Abstract:

This thesis consists of two papers in toric geometry. In Paper A we provide a complete classification up to isomorphism of all smooth convex lattice 3- polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining four are obtained as inverse stellar subdivisions of such polytopes. We derive a classification, up to isomorphism, of all complete embeddings of smooth toric threefolds in PN where N ≤ 15. Again we have in total 103 such embeddings. Of these, 99 are projective bundles embedded

APA, Harvard, Vancouver, ISO, and other styles

8

Codenotti, Giulia [Verfasser]. "Covering properties of lattice polytopes / Giulia Codenotti." Berlin : Freie Universität Berlin, 2020. http://d-nb.info/1205735569/34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Balletti, Gabriele. "Classifications and volume bounds of lattice polytopes." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-139823.

Full text

Abstract:

In this licentiate thesis we study relations among invariants of lattice polytopes, with particular focus on bounds for the volume.In the first paper we give an upper bound on the volume vol(P^*) of a polytope P^* dual to a d-dimensional lattice polytope P with exactly one interiorlattice point, in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp, and is achieved by the dual to a particular reflexive simplex. Our result implies a sharp upper bound on the volume of a d-dimensional reflexive polytope. In the second paper we classify the three-dimensional latti

APA, Harvard, Vancouver, ISO, and other styles

10

Akhtar, Mohammad Ehtisham. "Mutations of Laurent polynomials and lattice polytopes." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/28115.

Full text

Abstract:

It has been conjectured that Fano manifolds correspond to certain Laurent polynomials under Mirror Symmetry. This correspondence predicts that the regularized quantum period of a Fano manifold coincides with the classical period of a Laurent polynomial mirror. This correspondence is not one-to-one, as many different Laurent polynomials can have the same classical period; it should become one-to-one after imposing the correct equivalence relation on Laurent polynomials. In this thesis we introduce what we believe to be the correct notion of equivalence: this is algebraic mutation of Laurent pol

APA, Harvard, Vancouver, ISO, and other styles

More sources

Books on the topic "Lattice polytope"

1

Deza. Scale-isometric polytopal graphs in hypercubes and cubic lattices: Polytopes in hypercubes and Zn̳. Imperial College Press, 2004.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

2

1962-, Sturmfels Bernd, ed. Introduction to tropical geometry. American Mathematical Society, 2015.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

3

Hibi, Takayuki, and Akiyoshi Tsuchiya. Algebraic and Geometric Combinatorics on Lattice Polytopes - Proceedings of the Summer Workshop on Lattice Polytopes. World Scientific Publishing Co Pte Ltd, 2019.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

4

Associahedra Tamari Lattices And Related Structures Tamari Memorial Festschrift. Birkh User, 2012.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Lattice polytope"

1

Becker, Anja, and Thijs Laarhoven. "Efficient (Ideal) Lattice Sieving Using Cross-Polytope LSH." In Progress in Cryptology – AFRICACRYPT 2016. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31517-1_1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Deza, Antoine, Komei Fukuda, Tomohiko Mizutani, and Cong Vo. "On the Face Lattice of the Metric Polytope." In Discrete and Computational Geometry. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-44400-8_12.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Subramani, K. "On Identifying Simple and Quantified Lattice Points in the 2SAT Polytope." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45470-5_21.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Bruns, Winfried, and Joseph Gubeladze. "Multiples of lattice polytopes." In Springer Monographs in Mathematics. Springer New York, 2009. http://dx.doi.org/10.1007/b105283_3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Haase, Christian, Benjamin Lorenz, and Andreas Paffenholz. "Generating Smooth Lattice Polytopes." In Mathematical Software – ICMS 2010. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15582-6_51.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Ewald, Günter. "Lattice polytopes and fans." In Combinatorial Convexity and Algebraic Geometry. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-4044-0_5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Böröczky, Károly J., and Monika Ludwig. "Valuations on Lattice Polytopes." In Lecture Notes in Mathematics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51951-7_8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Whitcher, Ursula. "Reflexive Polytopes and Lattice-Polarized K3 Surfaces." In Calabi-Yau Varieties: Arithmetic, Geometry and Physics. Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2830-9_3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Beck, Matthias, and Sinai Robins. "Counting Lattice Points in Polytopes: The Ehrhart Theory." In Computing the Continuous Discretely. Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2969-6_3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

De Loera, Jesús A. "The many aspects of counting lattice points in polytopes." In Facetten der Mathematik. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55656-6_7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Lattice polytope"

1

Castillo, Federico. "A pithy look at the polytope algebra." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Cavey, Daniel. "Restrictions on the singularity content of a Fano polygon." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Steinmeyer, Johanna. "On the faces of simple polytopes." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0025.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Suyama, Yusuke. "Notes on toric Fano varieties associated to building sets." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0026.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Tran, Bach Le. "A Reider-type result for smooth projective toric surfaces." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0027.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Zheng, Hailun. "Face enumeration on flag complexes and flag spheres." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0028.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Hofscheier, Johannes. "Introduction to toric geometry with a view towards lattice polytopes." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Jochemko, Katharina. "A brief introduction to valuations on lattice polytopes." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Alexandersson, Per, and Elie Alhajjar. "Ehrhart positivity and Demazure characters." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Balletti, Gabriele, and Christopher Borger. "Families of 3-dimensional polytopes of mixed degree one." In Summer Workshop on Lattice Polytopes. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811200489_0004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!