## Abstract

Let I_{n} denote the set of inversion sequences of length n. In this paper, we enumerate members of I_{n} represented using positive integers according to parameters which track the number of runs and successions of letters of a given parity. To this end, we consider a four-parameter joint distribution on I_{n} and derive several general results for this distribution, providing further treatment of some particular cases. In order to prove our results, we make use of a non-standard generating function which allows for the system of recurrences satisfied by various refinements of the aforementioned joint distribution to be translated into a system of linear differential equations that can be solved explicitly. Finally, the more general problem of enumerating the members of I_{n} according to adjacencies involving two elements that are equivalent modulo m is considered.

Original language | English |
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Pages (from-to) | 24-39 |

Number of pages | 16 |

Journal | Discrete Applied Mathematics |

Volume | 330 |

DOIs | |

State | Published - 15 May 2023 |

### Bibliographical note

Publisher Copyright:© 2022 Elsevier B.V.

## Keywords

- Combinatorial statistic
- Generating function
- Inversion sequence
- Parity succession

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics