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arXiv · 2608.12731

The multiplicity sequence of monomial ideals

Sudipta Das·Jonathan Montaño·Aniketh Sivakumar
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Abstract

We give a convex-geometric formula for the multiplicity sequence of a monomial ideal in terms of mixed volumes of polytopes constructed from its Newton polyhedron. We also construct a counterexample to a conjecture of Achilles and Manaresi proposing a different volume formula for the multiplicity sequence. Finally, we derive a mixed-volume formula for the mixed multiplicities of arbitrary monomial ideals.

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Sudipta Das, Jonathan Montaño, Aniketh Sivakumar. 2026-08-13. The multiplicity sequence of monomial ideals. https://arxiv.org/abs/2608.12731

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