Small Forbidden Configurations

In the present paper we continue the work begun by Sauer, Perles, Shelah and Anstee on forbidden configurations of 0–1 matrices. We give asymptotically exact bounds for all possible 2 × l forbidden submatrices and almost all 3 × l ones. These bounds are improvements of the general bounds, or else new constructions show that the general bound is best possible. It is interesting to note that up to the present state of our knowledge every forbidden configuration results in polynomial asymptotic.

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