Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Monday 4
Combinatorics
Karen Yeats
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
On intervals of the consecutive pattern poset
Sergi Elizalde  1  , Peter R. W. Mcnamara  2  
1 : Department of Mathematics, Dartmouth College, Hanover, NH 03755
2 : Dept of Math, Bucknell University, Lewisburg

The consecutive pattern poset is the infinite partially ordered set of all permutations where σ τ if τ has a subsequence of adjacent entries in the same relative order as the entries of σ. 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 Mo ̈bius function equal to zero. 



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