On the Positivity of Infinite Products Connected to Partitions with Even Parts Below Odd Parts and Copartitions

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2024-07-01 DOI:10.1007/s00026-024-00704-3

Hannah E. Burson, Dennis Eichhorn

引用次数: 0

Abstract

In this paper, we give a combinatorial proof of a positivity result of Chern related to Andrews’s \(\mathcal{E}\mathcal{O}^*\)-type partitions. This combinatorial proof comes after reframing Chern’s result in terms of copartitions.Using this new perspective, we also reprove an overpartition result of Chern by showing that it comes essentially “for free” from our combinatorial proof and some basic properties of copartitions. Finally, the application of copartitions leads us to more general positivity conjectures for families of both infinite and finite products, with a proof in one special case.

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论与偶数部分低于奇数部分的分区和共分区相连的无限积的实在性

在本文中，我们给出了一个与安德鲁斯（Andrews）的（\mathcal{E}\mathcal{O}^*\）型分区相关的车恩（Chern）的实在性结果的组合证明。利用这个新视角，我们还重新证明了车恩的一个超分区结果，证明它基本上是 "免费 "从我们的组合证明和共分区的一些基本性质中得到的。最后，协方的应用将我们引向无限和有限乘积族的更一般的实在性猜想，并在一个特例中得到证明。

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