Coxeter群中错排的对数凸性的组合证明
Combinatorial proof of the log-convexity for the derangements in the Coxeter groups
AI总结：
本文针对对称群、超八面体群和半超八面体群，采用组合方法证明错排数及偶、奇错排数序列的对数凸性。
摘要：
我们给出了对称群$\mathfrak{S}_n$、超八面体群$\mathfrak{B}_n$和半超八面体群$\mathfrak{D}_n$中错排数对数凸性的组合证明。我们还证明了$\mathfrak{S}_n$和$\mathfrak{B}_n$中偶错排数与奇错排数的序列均为对数凸的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
