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On Young tableau involutions and patterns in permutations
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

This thesis is dealing with the combinatorics of permutations in three different aspects. In the first two papers, two flavours of pattern avoiding permutations are examined and in the third paper Young tableaux, which are tightly related to permutations via representation theory, are studied.

A permutation is alternating if it is alternatingly rising and descending and doubly alternating if both itself and its inverse are alternating. In the first paper we give solutions to several interesting problems regarding pattern avoiding doubly alternating permutations, such as finding a bijection between 1234-avoiding permutations and 1234-avoiding doubly alternating permutations of twice the size.

The matrix representation of a permutation is a square 0-1-matrix such that every row and column has exactly one 1. A pre-permutation is a rectangular matrix which is a submatrix of a permutation matrix. In the second paper pre-permutations which can be extended to pattern avoiding permutations are examined. An general algorithm is presented which is subsequently used to solve many different cases.

The third paper deals with involutions on Young tableaux. There is a surprisingly large collection of relations among these involutions and in this paper we make an effort to study them systematically in order to create a coherent theory. The most interesting result is that for Littlewood Richardson tableaux, a3 = Id, where a is the composition of three different involutions: the first fundamental symmetry map, the reversal and the rotation involution.

##### Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2005. , p. 102
##### Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 993
Mathematics
##### Identifiers
ISBN: 9185457884 (print)OAI: oai:DiVA.org:liu-143580DiVA, id: diva2:1165023
##### Public defence
2005-12-19, Glashuset, hus B, Campus Valla, Linköping, 10:15 (English)
##### Opponent
Available from: 2017-12-13 Created: 2017-12-12 Last updated: 2018-01-17Bibliographically approved

#### Open Access in DiVA

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##### By organisation
Department of MathematicsThe Institute of Technology
Mathematics

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Cite
Citation style
• apa
• harvard1
• ieee
• modern-language-association-8th-edition
• vancouver
• oxford
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf