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 Events
University of Washington
Tue 16 Sep 2014, 4:00pm
Discrete Math Seminar
ESB 4133
Coxeter-Knuth Graphs and a signed Little map
ESB 4133
Tue 16 Sep 2014, 4:00pm-5:00pm

Abstract

We propose an analog of the Little map for reduced expressions for signed permutations. We show that this map respects the transition equations derived from Chevellay's formula on Schubert classes. We discuss many nice properties of the signed Little map which generalize recent work of Hamaker and Young in type A where they proved Lam's conjecture.   As a key step in this work, we define shifted dual equivalence graphs building on work of Assaf and Haiman and prove they can be characterized by axioms.   These graphs are closely related to both the signed Little map and to the Coxeter-Knuth relations of type B due to Kraskiewicz.
 
This talk is based on joint work with Zach Hamaker, Austin Roberts and Ben Young.
 
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Justin Chan
SFU
Tue 4 Nov 2014, 4:00pm
Discrete Math Seminar
ESB 4133
An infinite family of inv-Wilf-equivalent permutation pairs
ESB 4133
Tue 4 Nov 2014, 4:00pm-5:00pm

Abstract

Wilf-equivalence is one of the central concepts of pattern-avoiding permutations, and has been studied for more than thirty years. The two known infi nite families of Wilf-equivalent permutation pairs, due to Stankova-West and Backelin-West-Xin, both satisfy the stronger condition of shape-Wilf-equivalence. Dokos et al. recently studied a di fferent strengthening of Wilf-equivalence called inv-Wilf-equivalence, which takes account of the inversion number of a permutation. They conjectured that all inv-Wilf-equivalent permutation pairs arise from trivial symmetries. We disprove this conjecture by constructing an infi nite family of counterexamples derived from the permutation pair (231) and (312). The key to this construction is to generalize simultaneously the concepts of shape-Wilf-equivalence and inv-Wilf-equivalence. A further consequence is a proof of the recent Baxter-Jaggard conjecture on even-shape-Wilf-equivalent permutation pairs.
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