DOAJ Open Access 2020

On intervals of the consecutive pattern poset

Sergi Elizalde Peter R. W. McNamara

Lihat Sumber DOI

Abstrak

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.

Topik & Kata Kunci

Mathematics

Penulis (2)

Sergi Elizalde

Peter R. W. McNamara

Format Sitasi

APA MLA BibTeX

Elizalde, S., McNamara, P.R.W. (2020). On intervals of the consecutive pattern poset. https://doi.org/10.46298/dmtcs.6380

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6380

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6380
Akses: Open Access ✓