Combinatorial proof of the log-convexity for the derangements in the Coxeter groups

2020/11/18 by Dey, Hiranya Kishore, Ghosh, Subhajit
#05A05 #05A20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.09546

Abstract

We provide the combinatorial proofs of the log-convexity for the derangement numbers in the symmetric group \mathfrakS_n, hyperoctahedral group \mathfrakB_n, and the demihyperoctahedral group \mathfrakD_n. We also show that the sequences of the even and odd derangement numbers in \mathfrakS_n and \mathfrakB_n are log-convex.

Related

• Strong q-log-convexity of the Eulerian polynomials of Coxeter groups
• Two identities of derangements
• Log-concavity of the Excedance Enumerators in positive elements of Type\n A and Type B Coxeter Groups
• Convex elements and Steinberg's cross-sections
• Convex cocompactness for Coxeter groups