Bubble Lattices II: Combinatorics

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2025-02-07 DOI:10.1007/s00026-025-00743-4

Thomas McConville, Henri Mühle

引用次数: 0

Abstract

We introduce two simplicial complexes, the noncrossing matching complex and the noncrossing bipartite complex. Both complexes are intimately related to the bubble lattice introduced in our earlier article “Bubble Lattices I: Structure” (arXiv:2202.02874). We study these complexes from both an enumerative and a topological point of view. In particular, we prove that these complexes are shellable and give explicit formulas for certain refined face numbers. Lastly, we conjecture an intriguing connection of these refined face numbers to the so-called M-triangle of the shuffle lattice.

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泡格II：组合学

我们引入了两种简单复形，即非交叉匹配复形和非交叉二部复形。这两种配合物都与我们之前的文章“气泡晶格I：结构”（arXiv:2202.02874）中介绍的气泡晶格密切相关。我们从枚举和拓扑两个角度来研究这些复合体。特别地，我们证明了这些配合物是可壳的，并给出了某些精炼面数的显式公式。最后，我们推测这些精致的面数与洗牌晶格的所谓m三角形之间有一个有趣的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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