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.
|Journal||Discrete and Computational Geometry|
|State||Accepted/In press - 2022|
Bibliographical notePublisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Smooth polyominoes
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics