Akademik Veri Yönetim Sistemi
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2025 (SCI-Expanded, Scopus)
This paper is a continuation of the earlier work of Arslan et al. [6], who studied algebraic and combinatorial properties of the Mahonian numbers of type B, addressing questions raised in their paper "A combinatorial interpretation of Mahonian numbers of types B and D", published in the "Ramanujan Journal" (2025). We first give the Knuth-Netto formula and the generating function for the subdiagonal entries (on or below the main diagonal) of the Mahonian triangle of type B, followed by their combinatorial interpretations in terms of lattice paths, partitions, and tilings. We then introduce a q-analogue of the Mahonian numbers of type B, defined via a new statistic on permutations in the hyperoctahedral group Bn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_n$$\end{document}, and investigate its fundamental properties along with corresponding combinatorial interpretations. Finally, we provide a combinatorial proof that the q-analogue of the Mahonian numbers of type B forms a strongly q-log-concave sequence of polynomials in k, which implies that the classical Mahonian numbers of type B form a log-concave sequence in k and therefore unimodal.