2024/04/01 by Ming-Jian Ding, Jiang Zeng, Ding, Ming-Jian +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2404.01465
openalex publication_date 2024/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.