Geodesic
Exponential multivalued forbidden configurations
Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 1.

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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 $r > 3$.
DOI : 10.46298/dmtcs.6613
Classification : 05B20, 05D05 
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Dillon, Travis; Sali, Attila. Exponential multivalued forbidden configurations. Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 1. doi : 10.46298/dmtcs.6613. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6613/

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