论文标题
入口和阿诺德家族的更多徒
More bijections for Entringer and Arnold families
论文作者
论文摘要
Euler号$ e_n $（分别为入口编号$ e_ {n，k} $）列举了$ \ {1，\ dots，n \} $的交替（向上）排列（从$ k $开始。 Springer Number $ s_n $（分别Arnold编号$ s_ {n，k} $）列举了类型$ b $交替的排列（分别以$ k $开头）。 In this paper, using bijections we first derive the counterparts in {\em André permutations} and {\em Simsun permutations} for the Entringer numbers $(E_{n,k})$, and then the counterparts in {\em signed André permutations} and {\em type $B$ increasing 1-2 trees} for the Arnold numbers $（s_ {n，k}）$。
The Euler number $E_n$ (resp. Entringer number $E_{n,k}$) enumerates the alternating (down-up) permutations of $\{1,\dots,n\}$ (resp. starting with $k$). The Springer number $S_n$ (resp. Arnold number $S_{n,k}$) enumerates the type $B$ alternating permutations (resp. starting with $k$). In this paper, using bijections we first derive the counterparts in {\em André permutations} and {\em Simsun permutations} for the Entringer numbers $(E_{n,k})$, and then the counterparts in {\em signed André permutations} and {\em type $B$ increasing 1-2 trees} for the Arnold numbers $(S_{n,k})$.
