Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
On intervals of the consecutive pattern poset
Sergi Elizalde  1  , Peter R. W. Mcnamara  2  
1 : Department of Mathematics [Dartmouth]  -  Website
Dartmouth CollegeHanover, NH 03755-3551, USA -  États-Unis
2 : Department of Mathematics  -  Website
Bucknell University Lewisburg, PA 17837 -  États-Unis

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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