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The Anstee-Sali Conjecture on Forbidden Configurations

Combinatorics · posed by Richard Anstee, Attila Sali, 2005 · disproved

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Statement

For a forbidden configuration F, the Anstee-Sali conjecture predicts that forb(m, F) is Theta(m^(X(F)-1)), where X(F) comes from an explicit product construction. Disproved: the 4-uniform family on six vertices formed by a two-vertex core joined to the edges of a 4-cycle has X(F) = 4, so the conjecture predicts Theta(m^3), while a random-alteration argument gives Omega(m^(10/3)).

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  1. construction · #1

    GPT-5.6 Sol, with Pei Wu

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