The Frobenius Complexity of Hibi Rings

We study the Frobenius complexity of Hibi rings over fields of characteristic p. In particular, for a certain class of Hibi rings (which we call anticanonical level), we compute the limit of the Frobenius complexity as p goes to infinity. Further, we compute the limit Frobenius complexity of pairs (R,D) in the case when R is a Segre product of two polynomial rings and D is any divisor on Spec R, and in the case when when R is a Gorenstein Hibi ring and D is a torus invariant divisor on Spec R corresponding to edge of our poset P.