Enumeration of s-omino towers and row-convex k-omino towers
Publikationstyp
Journal Article
Date Issued
2021
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
24
Issue
3
Article Number
21.3.6
Citation
Journal of Integer Sequences 24 (3): 21.3.6 (2021)
Scopus ID
We first enumerate a generalization of domino towers that was proposed by Brown, which we call S-omino towers. We establish equations that the generating function must satisfy, and then apply the Lagrange inversion formula to find a closed formula for the number of towers. We also show a connection to generalized Dyck paths and describe an explicit bijection. Finally, we consider the set of row-convex k-omino towers, introduced by Brown, and calculate an exact generating function.
Subjects
Bijection
Convex polyomino
Domino
Lagrange inversion