Oriented posets, rank matrices and q-deformed Markov numbers

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-09-12 DOI:10.1016/j.disc.2024.114256

Ezgi Kantarcı Oğuz

引用次数: 0

Abstract

We define oriented posets with corresponding rank matrices, where linking two posets by an edge corresponds to matrix multiplication. In particular, linking chains via this method gives us fence posets, and taking traces gives us circular fence posets. As an application, we give a combinatorial model for q-deformed Markov numbers. We also resolve a conjecture of Leclere and Morier-Genoud and give several identities between circular rank polynomials.

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定向正集、秩矩阵和 q 变形马尔可夫数

我们定义了具有相应秩矩阵的定向集合，通过边将两个集合连接起来就相当于矩阵乘法。特别是，通过这种方法连接链可以得到栅栏集合，而通过迹则可以得到循环栅栏集合。作为应用，我们给出了 q 变形马尔可夫数的组合模型。我们还解决了勒克莱尔和莫里埃-杰努德的一个猜想，并给出了循环秩多项式之间的几个同分异构体。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.