Work

The non-pure dual exchange property in low dimensions

Year: 2026

Type: article

Abstract: We investigate monomial ideals satisfying the non-pure dual exchange property, a notion introduced in connection with componentwise polymatroidal ideals. Our contributions are twofold. First, we show that in two variables, every integrally closed monomial ideal satisfies this property; as a consequence, we characterize polymatroidal ideals in two variables. Second, for strongly stable (Borel) ideals in three variables, we establish a practical criterion: it suffices to verify the defining condition only for the Borel generators, and this verification reduces to simple inequalities involving the degrees in the second and third variables.

Source: Communications in Algebra

DOI: 10.1080/00927872.2026.2754793

Authors: Reza Abdolmaleki, Shinya Kumashiro

Institutions: Institute for Advanced Studies in Basic Sciences, Lahore University of Management Sciences, Osaka Institute of Technology

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green