A Sauer-Shelah-Perles Lemma for Lattices

Stijn Cambie, Bogdan Chornomaz, Zeev Dvir, Yuval Filmus, Shay Moran

Abstract: We study lattice-theoretical extensions of the celebrated Sauer–Shelah–Perles Lemma. We conjecture that a general Sauer–Shelah–Perles Lemma holds for a lattice if and only if the lattice is relatively complemented, and prove partial results towards this conjecture.