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

Hiranya Kishore Dey; Subhajit Ghosh

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

Combinatorics 2023-08-16 v2

Authors: Hiranya Kishore Dey , Subhajit Ghosh

Abstract

We provide the combinatorial proofs of the log-convexity for the derangement numbers in the symmetric group $\mathfrak{S}_n$ , hyperoctahedral group $\mathfrak{B}_n$ , and the demihyperoctahedral group $\mathfrak{D}_n$ . We also show that the sequences of the even and odd derangement numbers in $\mathfrak{S}_n$ and $\mathfrak{B}_n$ are log-convex.

Keywords

log-convexity derangement numbers symmetric group hyperoctahedral group demihyperoctahedral group coxeter groups combinatorial proof

Cite

@article{arxiv.2011.09546,
  title  = {Combinatorial proof of the log-convexity for the derangements in the Coxeter groups},
  author = {Hiranya Kishore Dey and Subhajit Ghosh},
  journal= {arXiv preprint arXiv:2011.09546},
  year   = {2023}
}

Comments

The mapping that is defined in Theorem 3.12 is not injective. Hence, the proof is not complete

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

Abstract

Keywords

Cite

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