Regularity and counting lemmas for multidimensional matrices
Combinatorics
2019-09-12 v1
Abstract
In the present paper we propose generalizations of the regularity and counting lemmas for multidimensional matrices under a finite alphabet. Firstly, we prove a variant of a multidimensional regularity lemma with the help of a translation of -regularity from graphs to matrices. Next, we state that this -regularity is sufficient for obtaining a matrix analogue of the counting lemma for -dimensional matrices but not for higher-dimensional cases. Finally, we introduce -regular patterns that allow us to deduce a multidimensional counting lemma.
Cite
@article{arxiv.1909.04858,
title = {Regularity and counting lemmas for multidimensional matrices},
author = {Anna A. Taranenko},
journal= {arXiv preprint arXiv:1909.04858},
year = {2019}
}