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combinatorics / Extremal set theory

The Anstee-Sali Conjecture on Forbidden Configurations

For a forbidden configuration $F$, the Anstee-Sali conjecture predicts that $\mathrm{forb}(m, F)$ is $\Theta\left(m^{X(F)-1}\right)$, 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 $\Omega(m^{\frac{10}{3}})$.

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combinatoricsAug 7, 2026Significance 20/100Registry: unreviewed

The Anstee-Sali Conjecture on Forbidden Configurations

Prior state unknown→disproved

For a forbidden configuration $F$, the Anstee-Sali conjecture predicts that $\mathrm{forb}(m, F)$ is $\Theta\left(m^{X(F)-1}\right)$, 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^{\frac{…

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For a forbidden configuration $F$, the Anstee-Sali conjecture predicts that $\mathrm{forb}(m, F)$ is $\Theta\left(m^{X(F)-1}\right)$, 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 $\Omega(m^{\frac{10}{3}})$.

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