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arXiv · 2606.04653

The sorting-Denert statistic

Shao-Hua Liu
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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.

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Shao-Hua Liu. 2026-06-03. The sorting-Denert statistic. https://arxiv.org/abs/2606.04653

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