Generalized Newton complementary duals of monomial ideals

Abstract

Given a monomial ideal in a polynomial ring over a field, we define the generalized Newton complementary dual of the given ideal. We show good properties of such duals including linear quotients and isomorphisms between the special fiber rings. We construct the cellular free resolutions of duals of strongly stable ideals generated in the same degree. When the base ideal is generated in degree two, we provide an explicit description of cellular free resolution of the dual of a compatible generalized stable ideal.

Characterization and Newton Complementary Dual of Quasi $f$-Ideals

“…After that, Doria and Simis [6] were examined different properties of Newton complementary dual. Ansaldi, Lin, and Shin [2] investigated the Newton complementary duals of monomial ideals.…”