Geodesic
Alternating permutations with restrictions and standard Young tableaux
The electronic journal of combinatorics, Tome 19 (2012) no. 2
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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 $(n+2,n,n-2)$.
DOI : 10.37236/2306
Classification : 05E10, 05A05, 05C30
Mots-clés : alternating permutation, pattern avoiding, Yamanouchi word, standard Young tableau, shifted standard Young tableau 
@article{10_37236_2306,
     author = {Yuexiao Xu and Sherry H. F. Yan},
     title = {Alternating permutations with restrictions and standard {Young} tableaux},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {2},
     doi = {10.37236/2306},
     zbl = {1253.05143},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2306/}
}
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%A Sherry H. F. Yan
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Yuexiao Xu; Sherry H. F. Yan. Alternating permutations with restrictions and standard Young tableaux. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2306

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