### Abstract

Language | English |
---|---|

Article number | P2.2 |

Number of pages | 27 |

Journal | The Electronic Journal of Combinatorics |

Volume | 21 |

Issue number | 2 |

Publication status | Published - 1 Apr 2014 |

### Fingerprint

### Keywords

- stack sorting
- revstack
- descent polynomial

### Cite this

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**Revstack sort, zigzag patterns, descent polynomials of t-revstack sortable permutations, and Steingrímsson's sorting conjecture.** / Dukes, Mark.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Revstack sort, zigzag patterns, descent polynomials of t-revstack sortable permutations, and Steingrímsson's sorting conjecture

AU - Dukes, Mark

PY - 2014/4/1

Y1 - 2014/4/1

N2 - In this paper we examine the sorting operator T(LnR)=T(R)T(L)n. Applying this operator to a permutation is equivalent to passing the permutation reversed through a stack. We prove theorems that characterise t-revstack sortability in terms of patterns in a permutation that we call zigzag patterns. Using these theorems we characterise those permutations of length n which are sorted by t applications of T for t=0,1,2,n−3,n−2,n−1. We derive expressions for the descent polynomials of these six classes of permutations and use this information to prove Steingrímsson's sorting conjecture for those six values of t. Symmetry and unimodality of the descent polynomials for general t-revstack sortable permutations is also proven and three conjectures are given.

AB - In this paper we examine the sorting operator T(LnR)=T(R)T(L)n. Applying this operator to a permutation is equivalent to passing the permutation reversed through a stack. We prove theorems that characterise t-revstack sortability in terms of patterns in a permutation that we call zigzag patterns. Using these theorems we characterise those permutations of length n which are sorted by t applications of T for t=0,1,2,n−3,n−2,n−1. We derive expressions for the descent polynomials of these six classes of permutations and use this information to prove Steingrímsson's sorting conjecture for those six values of t. Symmetry and unimodality of the descent polynomials for general t-revstack sortable permutations is also proven and three conjectures are given.

KW - stack sorting

KW - revstack

KW - descent polynomial

UR - http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i2p2

M3 - Article

VL - 21

JO - The Electronic Journal of Combinatorics

T2 - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

SN - 1077-8926

IS - 2

M1 - P2.2

ER -