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On random shifted standard Young tableaux and 132-avoiding sorting networks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6339-2230
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-4489-1920
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

National Category
Discrete Mathematics Probability Theory and Statistics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-235374OAI: oai:DiVA.org:kth-235374DiVA, id: diva2:1250656
Funder
Swedish Research Council, 621-2014-4780
Note

QC 20180926

Available from: 2018-09-24 Created: 2018-09-24 Last updated: 2018-09-26Bibliographically approved
In thesis
1. Limit shapes of standard Young tableaux and sorting networks via the Edelman-Greene correspondence
Open this publication in new window or tab >>Limit shapes of standard Young tableaux and sorting networks via the Edelman-Greene correspondence
2018 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of the following two articles.

  • New properties of the Edelman–Greene bijection. Edelman and Greene constructed a correspondence between reduced words of the reverse permutation and standard Young tableaux. We prove that for any reduced word the shape of the region of the insertion tableau containing the smallest possible entries evolves exactly as the upper-left component of the permutation’s (Rothe) diagram. Properties of the Edelman–Greene bijection restricted to 132-avoiding and 2143-avoiding permutations are presented. We also consider the Edelman-Greene bijection applied to non-reduced words.
  • 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 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.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2018. p. 29
Series
TRITA-SCI-FOU ; 2018:43
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-235376 (URN)978-91-7729-959-2 (ISBN)
Presentation
2018-10-17, F11, Lindstedtsvägen 22, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20180926

Available from: 2018-09-26 Created: 2018-09-24 Last updated: 2018-09-26Bibliographically approved

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CiteExportLink to record
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Citation style
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