On Young tableau involutions and patterns in permutations
Abstract
This thesis deals with three different aspects of the combinatorics of permutations. In the first two papers, two flavours of pattern avoiding permutations are examined; and in the third paper Young tableaux, which are closely related to permutations via representation theory, are studied. In the first paper we give solutations to several interesting problems regarding pattern avoiding doubly alternating permutations, such as finding a bijection between 1234avoiding permutations and 1234avoiding doubly alternating permutations of twice the size. In the second paper partial permutations which can be extended to pattern avoiding permutations are examined. A general algorithm is presented which is subsequently used to solve many different problems. The third paper deals with involutions on Young tableaux. There is a surprisingly large collection of relations among these involutions and in the paper we make the effort to study them systematically in order to create a coherent theory. The most interesting result is that for LittlewoodRichardson tableaux, $a^3=1$, wher5e $a$ is the composition of three different involutions: the fundamental symmetry map, the reversal and rotation involutions.
 Publication:

arXiv eprints
 Pub Date:
 August 2009
 DOI:
 10.48550/arXiv.0908.0255
 arXiv:
 arXiv:0908.0255
 Bibcode:
 2009arXiv0908.0255O
 Keywords:

 Mathematics  Combinatorics;
 05A15 (Primary);
 05A17 05E10 (Secondary)
 EPrint:
 Ph.D. thesis, Link\"opings Universitet, 2005