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{\bf Richard Anstee, Ron Ferguson, Attila Sali}
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{\bf Small Forbidden Configurations II}
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The present paper
continues the work begun by Anstee, Griggs and Sali on
small forbidden configurations. In the notation of (0,1)-matrices, we
consider a
(0,1)-matrix $F$ (the forbidden configuration), an $m\times n$
(0,1)-matrix $A$ with no repeated
columns which has no submatrix which is a row and column permutation
of $F$, and seek
bounds on $n$ in terms of $m$ and $F$. We give new exact
bounds for some  $2\times l$ forbidden configurations and some
asymptotically exact bounds for some other $2\times l$ forbidden
configurations. We frequently employ graph theory and in one case
develop a new vertex ordering for directed graphs that generalizes
R\'edei's Theorem for Tournaments. One can now imagine that
exact bounds could be available for all $2\times l$
forbidden configurations. Some progress is reported for
$3\times l$ forbidden configurations. These bounds are improvements
of the
general bounds obtained by Sauer, Perles and Shelah, Vapnik and
Chervonenkis. 


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