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Oct 4, 2020 at 19:59 comment added Sam Hopkins Another very nice answer! I guess there is not exactly a name for this situation though ("the standard monomials form a basis of the semigroup ring of the cone over the polytope" is not so snappy). I also wonder if anything interesting can be said about zeta polynomials of posets beyond distributive lattices from this Ehrhart perspective.
Oct 4, 2020 at 19:08 history answered Gjergji Zaimi CC BY-SA 4.0