The Inversion Statistic in Derangements and in other Permutations with a Prescribed Number of Fixed Points
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
Fields of Study & Subjects
Bayesian Methods and Mixture Models
Advanced Combinatorial Mathematics
Algorithms and Data Compression
Publication details
- Journal / source
- The Electronic Journal of Combinatorics
- Volume
- 33
- Issue
- 2
- Publication date
- 21 May 2026
- Language
- EN