1. More bijections for Entringer and Arnold families
- Author
-
Heesung Shin and Jiang Zeng
- Subjects
Combinatorics ,05A05, 05A15, 05A19 ,symbols.namesake ,FOS: Mathematics ,symbols ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,Type (model theory) ,Bijection, injection and surjection ,Euler number ,Mathematics - Abstract
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 Andr\'e permutations} and {\em Simsun permutations} for the Entringer numbers $(E_{n,k})$, and then the counterparts in {\em signed Andr\'e permutations} and {\em type $B$ increasing 1-2 trees} for the Arnold numbers $(S_{n,k})$., Comment: 21 pages, 3 figures, 6 tables
- Published
- 2021