Year: 2026
Type: preprint
Abstract: Denert's statistic is a classical Mahonian statistic on permutations. Together with the excedance number, it forms an Euler--Mahonian pair, a result first conjectured by Denert and later proved by Foata and Zeilberger. Motivated by this classical result, we introduce the sorting-Denert statistic, a sorting-index analogue of Denert's statistic. It is obtained by replacing, in Denert's statistic, the inversion number of the non-excedance-letter subsequence with its sorting index. We prove that the sorting-Denert statistic, together with the excedance number, forms a new Euler--Mahonian pair.
Source: arXiv (Cornell University)
Author: Liu, Shao-Hua
Institution: Guangdong University Of Finances and Economics
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6468307436
OpenAlex ID: W7163560094
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