On random shifted standard Young tableaux and 132-avoiding sorting networks

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 li...

Full description

Saved in:
Bibliographic Details
Published inSéminaire lotharingien de combinatoire no. 82
Main Authors Linusson, Svante, Potka, Samu, Sulzgruber, Robin
Format Journal Article
LanguageEnglish
Published 2019
Subjects
random 132-avoiding sorting networks
Shifted standard Young tableaux
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1286-4889
1286-4889