  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.
