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Pattern Avoidance in Alternating Sign Matrices
Linköping University, Department of Mathematics.
2006 (English)Independent thesis Basic level (professional degree), 20 points / 30 hpStudent thesis
Abstract [en]

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.

Place, publisher, year, edition, pages
Matematiska institutionen , 2006. , 51 p.
Keyword [en]
Combinatorics, Alternating Sign Matrix, Permutation, Restricted permutation, Permutation pattern, Pattern avoidance, Schröder number
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-7936ISRN: LiTH-MAT-EX--06/15--SEOAI: oai:DiVA.org:liu-7936DiVA: diva2:22841
Uppsok
fysik/kemi/matematik
Supervisors
Examiners
Available from: 2006-12-21 Created: 2006-12-21

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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More styles
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  • de-DE
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  • nn-NB
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  • Other locale
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Output format
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