Kantarcı Oğuz, Ezgi
(2019)
*Descent polynomials, peak polynomials and an involution on permutations.*
Seminaire Lotharingien de Combinatoire
(82).
ISSN 1286-4889

## Abstract

The size of the set of all permutations of n with a given descent set is a polynomial in n, called the descent polynomial. Similarly, the size of the set of all permutations of n with a given peak set, adjusted by a power of 2 gives a polynomial in n, called the peak polynomial. We give a unitary expansion of descent polynomials in terms of peak polynomials. Then we use this expansion, along with an involution that flips the initial segment of a permutation, to give a combinatorial interpretation of the coefficients of the peak polynomial in a binomial basis, thus giving a new proof of the peak polynomial positivity conjecture.

Item Type: | Article |
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Uncontrolled Keywords: | descent; peak; permutation; spike |

Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |

Depositing User: | Ezgi Kantarcı Oğuz |

Date Deposited: | 07 Aug 2023 11:48 |

Last Modified: | 07 Aug 2023 11:48 |

URI: | https://research.sabanciuniv.edu/id/eprint/47385 |