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.
Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-7936 |
Date | January 2006 |
Creators | Johansson, Robert |
Publisher | Linköpings universitet, Matematiska institutionen, Matematiska institutionen |
Source Sets | DiVA Archive at Upsalla University |
Language | English |
Detected Language | English |
Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
Format | application/pdf |
Rights | info:eu-repo/semantics/openAccess |
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