Work

The Inversion Statistic in Derangements and in other Permutations with a Prescribed Number of Fixed Points

Year: 2026

Type: article

Abstract: We study how the inversion statistic is influenced by fixed points in a permutation. For each $n\in\mathbb{N}$, and each $k\in\{0,1,\cdots, n\}$, let $P_n^{(k)}$ denote the uniform probability measure on the set of permutations in $S_n$ with exactly $k$ fixed points. We obtain an exact formula for the expected number of inversions under the measure $P_n^{(k)}$ as well as for $P_n^{(k)}(\sigma^{-1}_i<\sigma^{-1}_j)$, for $1\le i

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/14250

Author: Ross Pinsky

Institution: Technion – Israel Institute of Technology

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4415030244

FWCI:

Cites:

Cited by:

Related to: