Ming-Jian Ding, Jiang Zeng
Published 2024-04-01Version 1
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.
$k$-partial permutations and the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebra
Statistics of Partial Permutations via Catalan matrices
The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations
![QR code for arXiv:2404.01465 [math.CO]](http://oss.arxitics.com/images/favicon.svg)