一些多变量多项式的经典续分，推广 Genocchi 数和 Genocchi 中值数

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-09-05 DOI:10.1016/j.aam.2024.102756

Bishal Deb , Alan D. Sokal

引用次数: 0

摘要

D-permutation 是 [2n] 的一种置换，对于所有 k 均满足 2k-1≤σ(2k-1)和 2k≥σ(2k)；它们为 Genocchi 数和中位 Genocchi 数提供了一种组合模型。我们为一些多变量多项式找到了斯蒂尔杰斯型和瑟隆型续分数，这些多变量多项式枚举了与大量（有时是无限量）同时测量循环状态、记录状态、交叉和嵌套的统计量有关的 D 型迭代。

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Classical continued fractions for some multivariate polynomials generalizing the Genocchi and median Genocchi numbers

A D-permutation is a permutation of $[2 n]$ satisfying $2 k - 1 \leq σ (2 k - 1)$ and $2 k \geq σ (2 k)$ for all k; they provide a combinatorial model for the Genocchi and median Genocchi numbers. We find Stieltjes-type and Thron-type continued fractions for some multivariate polynomials that enumerate D-permutations with respect to a very large (sometimes infinite) number of simultaneous statistics that measure cycle status, record status, crossings and nestings.

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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.