Multi-Symbol Forbidden Configurations
Keaton Ellis, Baian Liu, Attila Sali

TL;DR
This paper advances the understanding of forbidden configurations in multi-symbol matrices by introducing new lower bounds, upper bounds, and techniques, including graph theory methods, to analyze the growth of such matrices.
Contribution
It introduces new constructions for lower bounds, a novel upper bound technique, and applies graph theory to derive asymptotic bounds for multi-symbol forbidden matrices.
Findings
Established new asymptotic bounds for various matrix configurations
Developed a graph-based representation of induction techniques
Provided bounds for block matrices with constant rows
Abstract
An -matrix is a matrix with symbols in . A matrix is simple if it has no repeated columns. Let the support of a matrix , be the largest simple matrix such that every column in is in . For a family of -matrices , we define as the maximum number of columns of an -rowed, -matrix such that is not a row-column permutation of for all . While many results exist for , there are fewer for larger numbers of symbols. We expand on the field of forbidding matrices with -symbols, introducing a new construction for lower bounds of the growth of (with respect to ) that is applicable to matrices that are either not simple or have a constant row. We also introduce a new upper bound restriction that helps with avoiding…
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