Alternating Permutations with Restrictions and Standard Young Tableaux

Abstract. In this paper, we establish bijections between the set of 4123-avoiding 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).