Alternating permutations with restrictions and standard young tableaux

Abstract

In this paper, we establish 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 show that 4123-avoiding up-down alternating permutations of length 2n+1 are in one-to-one correspondence with standard Young tableaux of shape (n + 1, n,n- 1), and 4123-avoiding up-down alternating permutations of length 2n are in bijection with shifted standard Young tableaux of shape (n + 2,n, n - 2).