Cakić, N.Mansour, T.Yıldırım, Gökhan2023-02-222023-02-222022-04-271661-8270http://hdl.handle.net/11693/111609We 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.EnglishBondary verticesInterior verticesKernel methodPolyominoesArticle10.1007/s11786-022-00528-5