自修正差分上升序列

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-06-20 DOI:10.1016/j.aam.2025.102929

Giulio Cerbai , Anders Claesson , Bruce E. Sagan

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引用次数: 0

摘要

上升序列在菲什伯恩构造组合学中起着关键作用。差分上升序列是用d-上升序列代替上升序列得到的自然推广。我们最近将所谓的hat映射扩展到差分上升序列，并且自修正差分上升序列是该映射下的不动点。我们对自修正差分上升序列进行了刻画，并用一定的广义斐波那契多项式对其进行了枚举。进一步，我们描述了d-Fishburn排列的相应子集。

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Self-modified difference ascent sequences

Ascent sequences play a key role in the combinatorics of Fishburn structures. Difference ascent sequences are a natural generalization obtained by replacing ascents with d-ascents. We have recently extended the so-called hat map to difference ascent sequences, and self-modified difference ascent sequences are the fixed points under this map. We characterize self-modified difference ascent sequences and enumerate them in terms of certain generalized Fibonacci polynomials. Furthermore, we describe the corresponding subset of d-Fishburn permutations.

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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.