Mahonian-Stirling statistics for partial permutations
Combinatorics
2024-04-03 v1
Abstract
Recently Cheng et al. (Adv. in Appl. Math. 143 (2023) 102451) generalized the inversion number to partial permutations, which are also known as Laguerre digraphs, and asked for a suitable analogue of MacMahon's major index. We provide such a major index, namely, the corresponding maj and inv statistics are equidistributed, and exhibit a Haglund-Remmel-Wilson type identity. We then interpret some Jacobi-Rogers polynomials in terms of Laguerre digraphs generalizing Deb and Sokal's alternating Laguerre digraph interpretation of some special Jacobi-Rogers polynomials.
Cite
@article{arxiv.2404.01465,
title = {Mahonian-Stirling statistics for partial permutations},
author = {Ming-Jian Ding and Jiang Zeng},
journal= {arXiv preprint arXiv:2404.01465},
year = {2024}
}