Alternating permutations with restrictions and standard Young tableaux (Q456305)

Summary: 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 \((n+2,n,n-2)\).