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      A decomposition of column-convex polyominoes and two vertex statistics

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      Author(s)
      Cakić, N.
      Mansour, T.
      Yıldırım, Gökhan
      Date
      2022-04-27
      Source Title
      Mathematics in Computer Science
      Print ISSN
      1661-8270
      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.
      Keywords
      Bondary vertices
      Interior vertices
      Kernel method
      Polyominoes
      Permalink
      http://hdl.handle.net/11693/111609
      Published Version (Please cite this version)
      https://doi.org/10.1007/s11786-022-00528-5
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      • Department of Mathematics 712
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