Commutation classes are equivalence classes on words that are equivalent by a sequence of commutation relations; that is to say, relations of the form xy=yx. They provide a framework for studying the combinatorial properties of reduced expressions for Coxeter group elements (or for studying the associated roots). We show that the commutation classes for a reduced word of a permutation are in correspondence with certain tableaux and demonstrate interesting features of this correspondence.
A tableaux correspondence for commutation classes I
Apr. 22, 2008 2pm (MATH 350)
Lie Theory
Hugh Denoncourt (CU)
X
Commutation classes are equivalence classes on words that are equivalent by a sequence of commutation relations; that is to say, relations of the form xy=yx. They provide a framework for studying the combinatorial properties of reduced expressions for Coxeter group elements (or for studying the associated roots). We show that the commutation classes for a reduced word of a permutation are in correspondence with certain tableaux and demonstrate interesting features of this correspondence.
A tableaux correspondence for commutation classes II
Apr. 29, 2008 2pm (MATH 350)
Lie Theory
Dan Daly (DU)
X
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.
Reduced decompositions with few repetitions and permutation patterns
A tableaux correspondence for commutation classes I