Bijections around Springer numbers

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-05-16 DOI:10.1016/j.disc.2025.114570

Shaoshi Chen , Yang Li , Zhicong Lin , Sherry H.F. Yan

引用次数: 0

Abstract

Arnol'd proved in 1992 that Springer numbers enumerate the snakes, which are type B analogs of alternating permutations. Chen, Fan and Jia in 2011 introduced the labeled ballot paths and established a “hard” bijection with snakes. Callan conjectured in 2012 and Han–Kitaev–Zhang proved recently that rc-invariant alternating permutations are counted by Springer numbers. Very recently, Chen–Fang–Kitaev–Zhang investigated multi-dimensional permutations and proved that weakly increasing 3-dimensional permutations are also counted by Springer numbers. In this work, we construct a sequence of “natural” bijections linking the above four combinatorial objects.

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大约100个数字

Arnol在1992年证明了施普林格个数字列举了蛇，它们是交替排列的B型类似物。陈、范和贾在2011年引入了标记选票路径，并建立了一个带有蛇的“硬”投票。Callan在2012年推测，Han-Kitaev-Zhang最近证明了rc不变的交替排列是由施普林格个数来计数的。最近，Chen-Fang-Kitaev-Zhang研究了多维排列，并证明了弱递增的三维排列也可以用施普林格数来计数。在这项工作中，我们构建了一个连接上述四个组合对象的“自然”对射序列。

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.