A decomposition of column-convex polyominoes and two vertex statistics

Date
2022-04-27
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Source Title
Mathematics in Computer Science
Print ISSN
1661-8270
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Publisher
Springer
Volume
16
Issue
1
Pages
9-1 - 9-13
Language
English
Type
Article
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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 αon3 / 2 where αo≈ 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 α1n where α1≈ 1.17157287 …. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

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Keywords
Bondary vertices, Interior vertices, Kernel method, Polyominoes
Citation
Published Version (Please cite this version)