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Characterizing Steiner Systems via Betti Numbers of Monomial Ideals
Given a point set $[n]$ and a collection $B$ of $k$-subsets of $[n]$, we create a monomial ideal whose Betti numbers completely determine whether the pair $([n],B)$ is a Steiner system $S(t,k,n)$. In particular, our construction characterizes Steiner triple systems and Steiner quadruple systems sole
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