有色q-Stirling数和q-Lah数：一个新的观点继续

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-04-10 DOI:10.1016/j.aam.2025.102889

Sen-Peng Eu , Louis Kao , Juei-Yin Lin

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引用次数: 0

摘要

蔡和瑞迪提出了一个研究组合结构 S 的 q-analogue f(q) 的新框架。具体来说，其目的是找出 S 上的两个统计量和 S 的一个适当子集 S′，从而使 f(q) 代表 S′上的 q-(1+q)- 展开，并探索这种展开的正集和拓扑解释。Cai 和 Readdy 在此框架内提供了两种经典斯特林数的全面剖面图。在这项工作中，我们将蔡和雷迪的结果扩展到两种彩色 q-Stirling 数以及彩色 q-Lah 数。我们还简要讨论了 D 型的 q-Stirling 和 q-Lah 数。

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Colored q-Stirling and q-Lah numbers: A new view continued

Cai and Readdy proposed a new framework for studying the q-analogue

f (q)

of a combinatorial structure S. Specifically, the aim is to identify two statistics over S and a proper subset

S^{'}

of S such that

f (q)

represents the q-

(1 + q)

-expansion over

S^{'}

, and to explore the poset and topological interpretations of this expansion. Cai and Readdy provided comprehensive profiles for classical Stirling numbers of both kinds within this framework. In this work, we extend Cai and Readdy's results to colored q-Stirling numbers of both kinds, as well as colored q-Lah numbers. We also briefly discuss q-Stirling and q-Lah numbers of type D.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.