Smooth Column Convex Polyominoes

Toufik Mansour; Armend Sh Shabani

doi:10.1007/s00454-022-00405-9

Smooth Column Convex Polyominoes

Toufik Mansour, Armend Sh Shabani

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we introduce and study several statistics on some families of polyominoes, named smooth column convex polyominoes and lower/upper smooth column convex polyominoes. We find the generating function in each case according to half of the number of horizontal and vertical steps in the boundary of polyominoes. In particular, we show that the number of smooth column convex polyominoes with semi-perimeter n is asymptotic to 4n+43/(289πn3), as n→ ∞. In deriving our results, we solve various types of functional equations that are satisfied by the generating functions.

Original language	English
Pages (from-to)	525-539
Number of pages	15
Journal	Discrete and Computational Geometry
Volume	68
Issue number	2
DOIs	https://doi.org/10.1007/s00454-022-00405-9
State	Published - Sep 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Semi-perimeter
Smooth polyominoes

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-022-00405-9

Cite this

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ER -

Smooth Column Convex Polyominoes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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