Polynomial invariants from characters on the Hopf monoid of convex geometries count extremal and enriched extremal functions, unifying known reciprocities; supersolvable convex geometries are characterized by a common chamber in the maximal cones of their order complex.
Combinatorial Hopf algebras and gen- eralized Dehn-Sommerville relations
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Convex Geometries via Hopf Monoids: Combinatorial Invariants, Reciprocity, and Supersolvability
Polynomial invariants from characters on the Hopf monoid of convex geometries count extremal and enriched extremal functions, unifying known reciprocities; supersolvable convex geometries are characterized by a common chamber in the maximal cones of their order complex.