A decomposition of column-convex polyominoes and two vertex statistics

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buir.contributor.authorYıldırım, Gökhan
buir.contributor.orcidYıldırım, Gökhan|0000-0003-4399-7843
dc.citation.epage9-13en_US
dc.citation.issueNumber1en_US
dc.citation.spage9-1en_US
dc.citation.volumeNumber16en_US
dc.contributor.authorCakić, N.
dc.contributor.authorMansour, T.
dc.contributor.authorYıldırım, Gökhan
dc.date.accessioned2023-02-22T13:15:25Z
dc.date.available2023-02-22T13:15:25Z
dc.date.issued2022-04-27
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractWe 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.en_US
dc.description.provenanceSubmitted by Evrim Ergin (eergin@bilkent.edu.tr) on 2023-02-22T13:15:25Z No. of bitstreams: 1 A_decomposition_of_column-convex_polyominoes_and_two_vertex_statistics.pdf: 270225 bytes, checksum: f20936611df6fa56ce01072cc43ad265 (MD5)en
dc.description.provenanceMade available in DSpace on 2023-02-22T13:15:25Z (GMT). No. of bitstreams: 1 A_decomposition_of_column-convex_polyominoes_and_two_vertex_statistics.pdf: 270225 bytes, checksum: f20936611df6fa56ce01072cc43ad265 (MD5) Previous issue date: 2022-04-27en
dc.identifier.doi10.1007/s11786-022-00528-5en_US
dc.identifier.issn1661-8270
dc.identifier.urihttp://hdl.handle.net/11693/111609
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttps://doi.org/10.1007/s11786-022-00528-5en_US
dc.source.titleMathematics in Computer Scienceen_US
dc.subjectBondary verticesen_US
dc.subjectInterior verticesen_US
dc.subjectKernel methoden_US
dc.subjectPolyominoesen_US
dc.titleA decomposition of column-convex polyominoes and two vertex statisticsen_US
dc.typeArticleen_US

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