Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes
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| Author | : Takayuki Hibi |
| Publisher | : World Scientific |
| Total Pages | : 476 |
| Release | : 2019-05-30 |
| Genre | : Mathematics |
| ISBN | : 9811200491 |
This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.
| Author | : Takayuki Hibi |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 0 |
| Release | : 2019 |
| Genre | : Polytopes |
| ISBN | : 9789811200472 |
This volume consists of research papers and expository survey articles presented by the invited speakers of the workshop 'Algebraic and Geometric Combinatorics on Lattice Polytopes'. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further development of many research areas surrounding lattice polytopes. With the survey articles, research papers and open problems, graduate students can learn fundamental materials on lattice polytopes and researchers can find exciting activities and avenues for further exploration on lattice polytopes.
| Author | : Alexander M. Kasprzyk |
| Publisher | : Springer Nature |
| Total Pages | : 368 |
| Release | : 2022-06-08 |
| Genre | : Mathematics |
| ISBN | : 3030983277 |
This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics. Covering a diverse range of topics, including algebraic geometry, mirror symmetry, symplectic geometry, discrete geometry, and algebraic combinatorics, the common theme is the study of lattice polytopes. These fascinating combinatorial objects are a cornerstone of toric geometry and continue to find rich and unforeseen applications throughout mathematics. The workshop Interactions with Lattice Polytopes assembled many top researchers at the Otto-von-Guericke-Universität Magdeburg in 2017 to discuss the role of lattice polytopes in their work, and many of their presented results are collected in this book. Intended to be accessible, these articles are suitable for researchers and graduate students interested in learning about some of the wide-ranging interactions of lattice polytopes in pure mathematics.
| Author | : Vitor Balestro |
| Publisher | : Springer Nature |
| Total Pages | : 1195 |
| Release | : |
| Genre | : |
| ISBN | : 3031505077 |
| Author | : Andreas Paffenholz |
| Publisher | : |
| Total Pages | : 235 |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
| Author | : Gabriel Cunningham |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 272 |
| Release | : 2021-04-06 |
| Genre | : Education |
| ISBN | : 1470448971 |
The papers showcase the breadth of discrete geometry through many new methods and results in a variety of topics. Also included are survey articles on some important areas of active research. This volume is aimed at researchers in discrete and convex geometry and researchers who work with abstract polytopes or string C C-groups. It is also aimed at early career mathematicians, including graduate students and postdoctoral fellows, to give them a glimpse of the variety and beauty of these research areas. Topics covered in this volume include: the combinatorics, geometry, and symmetries of convex polytopes; tilings; discrete point sets; the combinatorics of Eulerian posets and interval posets; symmetries of surfaces and maps on surfaces; self-dual polytopes; string C C-groups; hypertopes; and graph coloring.
| Author | : Christian Haase |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 83 |
| Release | : 2021-07-21 |
| Genre | : Education |
| ISBN | : 1470447169 |
Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.
| Author | : Kaitlin Bruegge |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2023 |
| Genre | : |
| ISBN | : |
| Author | : L. Pachter |
| Publisher | : Cambridge University Press |
| Total Pages | : 440 |
| Release | : 2005-08-22 |
| Genre | : Mathematics |
| ISBN | : 9780521857000 |
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
| Author | : Michael Joswig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 332 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662051486 |
A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.
