The multiplicity sequence of every monomial ideal equals a sum of mixed volumes of polytopes constructed from its Newton polyhedron, a formula that also produces a counterexample to the Achilles-Manaresi conjecture.
Multiplicity for ideals of maximal analytic spread and intersection theory
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The multiplicity sequence of monomial ideals
The multiplicity sequence of every monomial ideal equals a sum of mixed volumes of polytopes constructed from its Newton polyhedron, a formula that also produces a counterexample to the Achilles-Manaresi conjecture.