Combinatorial generation via permutation languages. II. Lattice congruences

This paper deals with lattice congruences of the weak order on symmetric group, and initiates investigation cover graphs corresponding quotients. These also arise as skeleta so-called quotientopes, a family polytopes recently introduced by Pilaud Santos [Bull. Lond. Math. Soc., 51:406–420, 2019], which generalize permutahedra, associahedra, hypercubes several other polytopes. We prove that all these have Hamilton path, can be computed simple greedy algorithm. is an application our framework for exhaustively generating various classes combinatorial objects encoding them permutations. characterize are vertex-transitive or regular via their arc diagrams, give precise asymptotic counting results, we determine minimum maximum degrees.