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

University of Haifa

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	American 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

Keywords

Semi-perimeter
Smooth polyominoes

All Science Journal Classification (ASJC) codes

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

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10.1007/s00454-022-00405-9

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title = "Smooth Column Convex Polyominoes",

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.",

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N2 - 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.

AB - 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.

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KW - Smooth polyominoes

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DO - 10.1007/s00454-022-00405-9

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SP - 525

EP - 539

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

ER -

Smooth Column Convex Polyominoes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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