Pattern Avoidance in Alternating Sign Matrices
Independent thesis Basic level (professional degree), 20 points / 30 hpStudent thesis
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.
Combinatorics, Alternating Sign Matrix, Permutation, Restricted permutation, Permutation pattern, Pattern avoidance, Schröder number
IdentifiersURN: urn:nbn:se:liu:diva-7936ISRN: LiTH-MAT-EX--06/15--SEOAI: oai:DiVA.org:liu-7936DiVA: diva2:22841