### Abstract

Original language | English |
---|---|

Pages (from-to) | 118–126 |

Number of pages | 9 |

Journal | Discrete Mathematics |

Volume | 339 |

Issue number | 1 |

Early online date | 27 Aug 2015 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- permutation Poset
- shellability
- möbius function

### Cite this

*Discrete Mathematics*,

*339*(1), 118–126. https://doi.org/10.1016/j.disc.2015.08.004

}

*Discrete Mathematics*, vol. 339, no. 1, pp. 118–126. https://doi.org/10.1016/j.disc.2015.08.004

**Intervals of permutations with a fixed number of descents are shellable.** / Smith, Jason P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Intervals of permutations with a fixed number of descents are shellable

AU - Smith, Jason P.

PY - 2015

Y1 - 2015

N2 - The set of all permutations, ordered by pattern containment, is a poset. We present an order isomorphism from the poset of permutations with a fixed number of descents to a certain poset of words with subword order. We use this bijection to show that intervals of permutations with a fixed number of descents are shellable, and we present a formula for the Möbius function of these intervals. We present an alternative proof for a result on the Möbius function of intervals [1,π] such that π has exactly one descent. We prove that if π has exactly one descent and avoids 456123 and 356124, then the intervals [1,π] have no nontrivial disconnected subintervals; we conjecture that these intervals are shellable.

AB - The set of all permutations, ordered by pattern containment, is a poset. We present an order isomorphism from the poset of permutations with a fixed number of descents to a certain poset of words with subword order. We use this bijection to show that intervals of permutations with a fixed number of descents are shellable, and we present a formula for the Möbius function of these intervals. We present an alternative proof for a result on the Möbius function of intervals [1,π] such that π has exactly one descent. We prove that if π has exactly one descent and avoids 456123 and 356124, then the intervals [1,π] have no nontrivial disconnected subintervals; we conjecture that these intervals are shellable.

KW - permutation Poset

KW - shellability

KW - möbius function

UR - http://www.sciencedirect.com/science/journal/0012365X

U2 - 10.1016/j.disc.2015.08.004

DO - 10.1016/j.disc.2015.08.004

M3 - Article

VL - 339

SP - 118

EP - 126

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1

ER -