CU Algebraic Lie Theory Seminar

Reduced decompositions with few repetitions and permutation patterns

Dan Daly, University of Denver

Abstract

Recent work by Tenner has given interest in studying reduced decompositions of permutations with few repetitions. Tenner has shown if a permutation has a reduced decomposition with no repeated elements then one can say quite a bit about the downset of that permutation in the Bruhat Order and about which patterns the permutation avoids. We try to extend these results a bit by looking at permutations with one and two repeated elements. Using such reduced decompositions we obtain new counts for certain classes of pattern-avoiding permutations.