## Abstract

Inversion sequences of length n are positive integer sequences e_{1} e_{2} …e_{n} such that 1 ≤ e_{i} ≤ i for all 1 ≤ i ≤ n. These sequences are in bijection with the permutations of [n]. This paper focuses on the polyomino or barpgraph representation of the inversion sequences. More precisely, we study the distribution of lattice points on these polyominoes. We find the generating functions respect to the length, the number of interior vertices, corners, and vertices of a given degree. We also give simple explicit formulas for the total values of these parameters over all polyominoes of inversion sequences of length n. Throughout this work, we use symbolic computer algebra to facilitate the computations.

Original language | English |
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Journal | Quaestiones Mathematicae |

DOIs | |

State | Accepted/In press - 2024 |

### Bibliographical note

Publisher Copyright:© 2024 NISC (Pty) Ltd.

## Keywords

- generating function
- interior points
- Inversion sequences
- vertex degree

## ASJC Scopus subject areas

- Mathematics (miscellaneous)