Convex polytopes all of whose reverse lexicographic initial ideals are squarefree

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Toric Ideals Arising from Contingency Tables (2007, background): “We refer the reader to [12], [14] and [15] for further information.”
Existence of unimodular triangulations — positive results (2014, result): “Hibi and Ohsugi also proved that if all induced cycles (cycles without a chord) satisfy part (3) (they are balanced or have one more edge in one direction) then PA has a unimodular cover.”
Unimodality Questions for Integrally Closed Lattice Polytopes (2011, background): “It is easy to see that k is a (0, 1)-polytope that satisfies a system of inequalities as in the main theorem of [17], so it follows that k is compressed.”