## Abstract

An inversion sequence (x_{1}, …, x_{n}) is one such that 1 ≤ x_{i} ≤ i for all 1 ≤ i ≤ n. We first consider the joint distribution of the area and perimeter statistics on the set I_{n} of inversion sequences of length n represented as bargraphs. Functional equations for both the ordinary and exponential generating functions are derived from recurrences satisfied by this distri-bution. Explicit formulas for the generating functions are found in some special cases as are expressions for the totals of the respective statistics on I_{n}. A similar treatment is provided for the joint distribution on I_{n} for the statistics recording the number of levels, descents and ascents. Some connections are made between specific cases of this latter distribution and the Stirling numbers of the first kind and Eulerian numbers.

Original language | English |
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Pages (from-to) | 42-49 |

Number of pages | 8 |

Journal | Discrete Mathematics Letters |

Volume | 4 |

State | Published - 2020 |

### Bibliographical note

Publisher Copyright:© 2020 the authors.

## Keywords

- Bargraph
- Combinatorial statistic
- Inversion sequence

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics