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math.AC2026
The multiplicity sequence of monomial ideals
Sudipta Das, Jonathan Montaño, Aniketh Sivakumar
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 construc…
math.AC2024
Partial Betti splittings with applications to binomial edge ideals
A. V. Jayanthan, Aniketh Sivakumar, Adam Van Tuyl
We introduce the notion of a partial Betti splitting of a homogeneous ideal, generalizing the notion of a Betti splitting first given by Francisco, Hà, and Van Tuyl. Given a homoge…