2022/11/10 by Kirgizov, Sergey, José Luis Zaragoza Ramírez, Ramírez, José Luis
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2211.05460
openalex publication_date 2022/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the k-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding k consecutive 1's, also called generalized k-bonacci words. The polyominoes are very entrancing objects, considered in combinatorics and computer science. The study of polyominoes generates a rich source of combinatorial ideas. In this paper we study some properties of k-bonacci polyominoes. Specifically, we determine their recursive structure and, using this structure, we enumerate them according to their area, semiperimeter, and length of the corresponding words. We also introduce the k-bonacci graphs, then we obtain the generating functions for the total number of vertices and edges, the distribution of the degrees, and the total number of k-bonacci graphs that have a Hamiltonian cycle.