Maximal 2-dimensional binary words of bounded degree
Combinatorics
2025-05-21 v1 Formal Languages and Automata Theory
Abstract
Let d be an integer between 0 and 4, and W be a 2-dimensional word of dimensions h x w on the binary alphabet {0, 1}, where h, w in Z > 0. Assume that each occurrence of the letter 1 in W is adjacent to at most d letters 1. We provide an exact formula for the maximum number of letters 1 that can occur in W for fixed (h, w). As a byproduct, we deduce an upper bound on the length of maximum snake polyominoes contained in a h x w rectangle.
Cite
@article{arxiv.2505.13640,
title = {Maximal 2-dimensional binary words of bounded degree},
author = {Alexandre Blondin Massé and Alain Goupil and Ralphael L'Heureux and Louis Marin},
journal= {arXiv preprint arXiv:2505.13640},
year = {2025}
}
Comments
49 pages, 36 figures