On intervals of the consecutive pattern poset

Sergi Elizalde (1) , Peter R. W. Mcnamara (2)

1 Department of Mathematics [Dartmouth]
2 Department of Mathematics

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.

Domaines: Combinatoire [math.CO]

Sergi Elizalde, Peter R. W. Mcnamara. On intervals of the consecutive pattern poset. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6380⟩. ⟨hal-02173380⟩