SFU

Tue 4 Nov 2014, 4:00pm
Discrete Math Seminar
ESB 4127

An infinite family of invWilfequivalent permutation pairs

ESB 4127
Tue 4 Nov 2014, 4:00pm5:00pm
Abstract
Wilfequivalence is one of the central concepts of patternavoiding permutations, and has been studied for more than thirty years. The two known infinite families of Wilfequivalent permutation pairs, due to StankovaWest and BackelinWestXin, both satisfy the stronger condition of shapeWilfequivalence. Dokos et al. recently studied a different strengthening of Wilfequivalence called invWilfequivalence, which takes account of the inversion number of a permutation. They conjectured that all invWilfequivalent permutation pairs arise from trivial symmetries. We disprove this conjecture by constructing an infinite family of counterexamples derived from the permutation pair (231) and (312). The key to this construction is to generalize simultaneously the concepts of shapeWilfequivalence and invWilfequivalence. A further consequence is a proof of the recent BaxterJaggard conjecture on evenshapeWilfequivalent permutation pairs.
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