<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>
| Identifer | oai:union.ndltd.org:UPSALLA/oai:DiVA.org:liu-7936 |
| Date | January 2006 |
| Creators | Johansson, Robert |
| Publisher | Linköping University, Department of Mathematics, Matematiska institutionen |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, text |
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