Permutations with Few Inversions

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2023-10-06 DOI:10.37236/12075

Anders Claesson, Atli Fannar Franklín, Einar Steingrímsson

引用次数: 0

Abstract

A curious generating function $S_0(x)$ for permutations of $[n]$ with exactly $n$ inversions is presented. Moreover, $(xC(x))^iS_0(x)$ is shown to be the generating function for permutations of $[n]$ with exactly $n-i$ inversions, where $C(x)$ is the generating function for the Catalan numbers.

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很少反转的排列

给出了一个奇异的生成函数$S_0(x)$，用于$[n]$的置换恰好具有$n$的反转。此外，$(xC(x))^iS_0(x)$被证明是具有正好$n-i$反转的$[n]$排列的生成函数，其中$C(x)$是加泰罗尼亚数字的生成函数。

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

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.