Variable dimension non-overlapping matrices
Abstract
Since some years, non-overlapping sets of strings (also called cross-bifix-free sets) have had an increasing interest in the frame of the researches about Theory of Codes. Recently some non-overlapping sets of strings with variable length were introduced. Moreover, the notion of non-overlapping strings has been naturally extended to the two dimensional case leading to several definitions of non-overlapping sets of matrices (or pictures). Starting from these results, in this paper we introduce non-overlapping sets of binary matrices having variable dimension. Indeed, we use non-overlapping variable length strings as rows of the matrices and imposing the avoidance of two consecutive patterns of length k, we get the desired sets of non-ovelapping matrices with variable dimension.
Cite
@article{arxiv.2006.05878,
title = {Variable dimension non-overlapping matrices},
author = {Elena Barcucci and Antonio Bernini and Renzo Pinzani},
journal= {arXiv preprint arXiv:2006.05878},
year = {2020}
}