A matrix is simple if it is a (0,1)-matrix and there are no repeated columns. Given a (0,1)-matrix $F$, we say a matrix $A$ has $F$ as a configuration, denoted $F\prec A$, if there is a submatrix of $A$ which is a row and column permutation of $F$. Let $|A|$ denote the number of columns of $A$. Let $\mathcal{F}$ be a family of matrices. We define the extremal function $\text{forb}(m, \mathcal{F}) = \max\{|A|\colon A \text{ is an }m-\text{rowed simple matrix and has no configuration } F\in\mathcal{F}\}$. We consider pairs $\mathcal{F}=\{F_1,F_2\}$ such that $F_1$ and $F_2$ have no common extremal construction and derive that individually each $\text{forb}(m, F_i)$ has greater asymptotic growth than $\text{forb}(m, \mathcal{F})$, extending research started by Anstee and Koch.
@article{10_37236_6902,
author = {Attila Sali and Sam Spiro},
title = {Forbidden families of minimal quadratic and cubic configurations},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {2},
doi = {10.37236/6902},
zbl = {1366.05114},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6902/}
}
TY - JOUR
AU - Attila Sali
AU - Sam Spiro
TI - Forbidden families of minimal quadratic and cubic configurations
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/6902/
DO - 10.37236/6902
ID - 10_37236_6902
ER -
%0 Journal Article
%A Attila Sali
%A Sam Spiro
%T Forbidden families of minimal quadratic and cubic configurations
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/6902/
%R 10.37236/6902
%F 10_37236_6902
Attila Sali; Sam Spiro. Forbidden families of minimal quadratic and cubic configurations. The electronic journal of combinatorics, Tome 24 (2017) no. 2. doi: 10.37236/6902
