## Abstract

We introduce a decomposition method for column-convex polyominoes and enumerate them in terms of two statistics: the number of internal vertices and the number of corners in the boundary. We first find the generating function for the column-convex polyominoes according to the horizontal and vertical half-perimeter, and the number of interior vertices. In particular, we show that the average number of interior vertices over all column-convex polyominoes of perimeter 2n is asymptotic to α_{o}n^{3 / 2} where α_{o}≈ 0.57895563 …. We also find the generating function for the column-convex polyominoes according to the horizontal and vertical half-perimeter, and the number of corners in the boundary. In particular, we show that the average number of corners over all column-convex polyominoes of perimeter 2n is asymptotic to α_{1}n where α_{1}≈ 1.17157287 ….

Original language | English |
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Article number | 9 |

Journal | Mathematics in Computer Science |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2022 |

### Bibliographical note

Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

## Keywords

- Bondary vertices
- Interior vertices
- Kernel method
- Polyominoes

## ASJC Scopus subject areas

- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics