A combinatorial interpretation of Mahonian numbers of type B

2024/04/07 by Hasan Arslan, Arslan, Hasan
Arts and Humanities · Social Sciences · #05A05 #05A15 #05A30 #Combinatorics (math.CO) #FOS: Mathematics #Historical Linguistics and Language Studies #Language, Linguistics, Cultural Analysis #Names, Identity, and Discrimination Research

paper · pdf · doi:10.48550/arxiv.2404.05099

openalex publication_date 2024/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first introduce the number of signed permutations with exactly k inversions, which is denoted by i_B(n,k) and called Mahonian numbers of type B. Then we provide a recurrence relation for the Mahonian numbers i_B(n,k). In addition, we give an explicit recursive description for the summation of inversions of all permutations in the hyperoctahedral group B_n, denoted by B_n. Furthermore, we enumerate the total number of inversions in permutations in the hyperoctahedral group B_n concretely with the help of an inversion statistic and a backward permutation concepts on B_n.

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