Smooth Column Convex Polyominoes

Toufik Mansour, Armend Sh Shabani

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
Pages (from-to)525-539
Number of pages15
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - Sep 2022


  • 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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