推广Genocchi数和中位数Genocchi数的多元多项式的经典连分数
Classical continued fractions for some multivariate polynomials generalizing the Genocchi and median Genocchi numbers
摘要：
D排列是$[2n]$的排列，对于所有$k$，满足$2k-1 \le σ(2k-1)$和$2k \ge σ(2k)$;它们提供了Genocchi数和中位数Genocchi数的组合模型。我们发现Stieltjes型和Thron型连分数的一些多元多项式，枚举D-排列相对于一个非常大的（有时是无限的）数量的同时统计，测量周期状态，记录状态，交叉和嵌套。
英文摘要：
A D-permutation is a permutation of $[2n]$ satisfying $2k-1 \le σ(2k-1)$ and $2k \ge σ(2k)$ for all $k$; they provide a combinatorial model for the Genocchi and median Genocchi numbers. We find Stieltjes-type and Thron-type continued fractions for some multivariate polynomials that enumerate D-permutations with respect to a very large (sometimes infinite) number of simultaneous statistics that measure cycle status, record status, crossings and nestings.
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。
