等变Ehrhart理论中的技术

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2023-11-21 DOI:10.1007/s00026-023-00673-z

Sophia Elia, Donghyun Kim, Mariel Supina

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引用次数: 0

摘要

等变Ehrhart理论推广了晶格点枚举的研究，也解释了在线性群作用下多面体的对称性。我们提出了在该领域应用的技术目录，包括分区分解，对称三角剖分，\(h^*\) -多项式的组合解释，以及不变非退化超曲面(不)存在的证明。我们将这些方法应用于包括超简单体、轨道多面体和图形分区多面体在内的几个族的例子，扩展了多面体库，其等变Ehrhart理论是已知的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Techniques in Equivariant Ehrhart Theory

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Techniques in Equivariant Ehrhart Theory

Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue of techniques with applications in this field, including zonotopal decompositions, symmetric triangulations, combinatorial interpretation of the \(h^*\)-polynomial, and certificates for the (non)existence of invariant nondegenerate hypersurfaces. We apply these methods to several families of examples including hypersimplices, orbit polytopes, and graphic zonotopes, expanding the library of polytopes for which their equivariant Ehrhart theory is known.

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来源期刊

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches