2013
DOI: 10.48550/arxiv.1307.1148
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Forbidden Families of Configurations

Abstract: A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)-matrix F , we say that a (0,1)-matrix A has F as a configuration if there is a submatrix of A which is a row and column permutation of F (trace is the set system version of a configuration). Let A denote the number of columns of A. Let F be a family of matrices. We define the extremal function forb(m, F) = max{ A : A is m-rowed simple matrix and has no configuration F ∈ F}. We consider some families F = {F 1 , F 2 , . . . , F t } such that… Show more

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Cited by 1 publication
(3 citation statements)
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“…In the present paper we continue the investigations started in [7]. Anstee and Koch determined forb(m, {F, G}) for all pairs {F, G}, where both members are minimal quadratics, that is both forb(m, F ) = Θ(m 2 ) and forb(m, G) = Θ(m 2 ), but no proper subconfiguration of F or G is quadratic.…”
Section: Whose Columns Consist Of All Possible Combinations Obtained ...mentioning
confidence: 63%
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“…In the present paper we continue the investigations started in [7]. Anstee and Koch determined forb(m, {F, G}) for all pairs {F, G}, where both members are minimal quadratics, that is both forb(m, F ) = Θ(m 2 ) and forb(m, G) = Θ(m 2 ), but no proper subconfiguration of F or G is quadratic.…”
Section: Whose Columns Consist Of All Possible Combinations Obtained ...mentioning
confidence: 63%
“…In addition to the configurations, we have included a list of all 2-fold and 3-fold products of I, I c and T that avoid these configurations. The list of constructions avoiding quadratic configurations comes from [7], and the lists for cubic configurations are proved in Section 2, with the statement that proves the result listed under "Proposition. "…”
Section: Product Constructionsmentioning
confidence: 98%
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