On random shifted standard Young tableaux and 132-avoiding sorting networks
Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1231-1258.

We study shifted standard Young tableaux (SYT). The limiting surface of uniformly random shifted SYT of staircase shape is determined, with the integers in the SYT as heights. This implies via properties of the Edelman–Greene bijection results about random 132-avoiding sorting networks, including limit shapes for trajectories and intermediate permutations. Moreover, the expected number of adjacencies in SYT is considered. It is shown that on average each row and each column of a shifted SYT of staircase shape contains precisely one adjacency.

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Accepted:
Published online:
DOI: 10.5802/alco.133
Classification: 60C05,  05E15,  68P10
Keywords: Shifted standard Young tableaux, random 132-avoiding sorting networks
Linusson, Svante 1; Potka, Samu 1; Sulzgruber, Robin 1

1 KTH Royal Institute of Technology Department of Mathematics Stockholm Sweden
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Linusson, Svante; Potka, Samu; Sulzgruber, Robin. On random shifted standard Young tableaux and 132-avoiding sorting networks. Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1231-1258. doi : 10.5802/alco.133. https://alco.centre-mersenne.org/articles/10.5802/alco.133/

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