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We study configuration spaces $C(n; p, q)$ of $n$ ordered unit squares in a$p$ by $q$ rectangle. Our goal is to estimate the Betti numbers for large $n$,$j$, $p$, and $q$. We consider sequences of area-normalized coordinates, where$(\frac{n}{pq}, \frac{j}{pq})$ converges as $n$, $j$, $p$, and $q$ approachinfinity. For every sequence that converges to a point in the "feasible region"in the $(x,y)$-plane, we show that the factorial growth rate of the Bettinumbers is the same as the factorial growth rate of $n!$. This implies that (1)the Betti numbers are vastly larger than for the configuration space of $n$ordered points in the plane, which have the factorial growth rate of $j!$, and(2) every point in the feasible region is eventually in the homological liquidregime.

Asymptotic Betti numbers for hard squares in the homological liquid regime