平衡的斯特林数字

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-07-05 DOI:10.1007/s00010-024-01087-9

Michael Maltenfort

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引用次数: 0

摘要

Hsu 和 Shiue（Adv Appl Math 20(3):366-384, 1998. https://doi.org/10.1006/aama.1998.0586）定义了广义斯特林数，其中包括各种组合量的特例。我们证明了这两种中心阶乘数是根本不同的新特例。我们的方法还发现了这两种中心阶乘数之间以前未曾认识到的联系。为了证明我们的主要结果，我们引入了平衡斯特林数，它是广义斯特林数的特例，可以进一步特化为任何一种中心阶乘数。

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Balanced Stirling numbers

Hsu and Shiue (Adv Appl Math 20(3):366–384, 1998. https://doi.org/10.1006/aama.1998.0586) defined generalized Stirling numbers, which include as special cases a wide variety of combinatorial quantities. We prove that the two kinds of central factorial numbers are fundamentally different new special cases. Our approach also yields a previously unrecognized connection between the two kinds of central factorial numbers. In order to prove our main results, we introduce balanced Stirling numbers, which specialize the generalized Stirling numbers and can be further specialized into either kind of central factorial numbers.

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.