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Pattern Avoidance in Alternating Sign Matrices

<p>This thesis is about a generalization of permutation theory. The concept of pattern avoidance in permutation matrices is investigated in a larger class of matrices - the alternating sign matrices. The main result is that the set of alternating sign matrices avoiding the pattern 132, is counted by the large Schröder numbers. An algebraic and a bijective proof is presented. Another class is shown to be counted by every second Fibonacci number. Further research in this new area of combinatorics is discussed.</p>

Identiferoai:union.ndltd.org:UPSALLA/oai:DiVA.org:liu-7936
Date January 2006
CreatorsJohansson, Robert
PublisherLinköping University, Department of Mathematics, Matematiska institutionen
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, text

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