episciences.org_6613_1639050664
1639050664
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
03
23
2021
vol. 23 no. 1
Combinatorics
Exponential multivalued forbidden configurations
Travis
Dillon
Attila
Sali
The forbidden number $\mathrm{forb}(m,F)$, which denotes the maximum number
of unique columns in an $m$-rowed $(0,1)$-matrix with no submatrix that is a
row and column permutation of $F$, has been widely studied in extremal set
theory. Recently, this function was extended to $r$-matrices, whose entries lie
in $\{0,1,\dots,r-1\}$. The combinatorics of the generalized forbidden number
is less well-studied. In this paper, we provide exact bounds for many
$(0,1)$-matrices $F$, including all $2$-rowed matrices when $r > 3$. We also
prove a stability result for the $2\times 2$ identity matrix. Along the way, we
expose some interesting qualitative differences between the cases $r=2$, $r =
3$, and $r > 3$.
03
23
2021
6613
arXiv:2006.16305
10.46298/dmtcs.6613
https://dmtcs.episciences.org/6613