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2018

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Consecutivepatterns.Pdf, Peter R. W. Mcnamara, Sergi Elizalde Feb 2018

Consecutivepatterns.Pdf, Peter R. W. Mcnamara, Sergi Elizalde

Peter R. W. McNamara

The consecutive pattern poset is the infinite partially ordered set of all permutations where sigma < tau if \tau has a subsequence of adjacent entries in the same relative order as the entries of sigma.  We study the structure of the intervals in this poset from topological, poset-theoretic, and enumerative perspectives. In particular, we prove that all intervals are rank-unimodal and strongly Sperner, and we characterize disconnected and shellable intervals. We also show that most intervals are not shellable and have Möbius function equal to zero.