2012/03/21 by Sherry H.F. Yan, Yan, Sherry H. F., Yuexiao Xu +1
Computer Science · Mathematics · #05A05 #05C30 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1203.4653
openalex publication_date 2012/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we give bijections between the set of 4123-avoiding down-up alternating permutations of length 2n and the set of standard Young tableaux of shape (n,n,n), and between the set of 4123-avoiding down-up alternating permutations of length 2n-1 and the set of shifted standard Young tableaux of shape (n+1, n, n-1) via an intermediate structure of Yamanouchi words. Moreover, we get the enumeration of 4123-avoiding up-down alternating permutations of even and odd length by presenting bijections between 4123-avoiding up-down alternating permutations and standard Young tableaux.