| Issue |
RAIRO-Theor. Inf. Appl.
Volume 59, 2025
Generation, enumeration and tiling
|
|
|---|---|---|
| Article Number | 8 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/ita/2025008 | |
| Published online | 08 September 2025 | |
Enumeration of Colored Tilings on Graphs via Generating Functions
1
Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
2
Department of Mathematics, Xavier University of Louisiana, New Orleans, LA 70125, USA
* Corresponding author: jlramirezr@unal.edu.co
Received:
10
January
2025
Accepted:
6
August
2025
In this paper, we study the problem of partitioning a graph into connected and colored components called blocks. Using bivariate generating functions and combinatorial techniques, we determine the expected number of blocks when the vertices of a graph G, for G in certain families of graphs, are colored uniformly and independently. Special emphasis is placed on graphs of the form G × Pn, where Pn is the path graph on n vertices. This case serves as a generalization of the problem of enumerating the number of tilings of an m × n grid using colored polyominoes.
Mathematics Subject Classification: 05A15 / 05A05
Key words: Tiling / polyomino / generating function
© The authors. Published by EDP Sciences, 2025
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