Inclusion Ideals Associated to Uniformly Increasing Hypergraphs

TL;DR

This paper introduces inclusion ideals linked to uniformly increasing hypergraphs, exploring their algebraic properties and providing bounds on their Castelnuovo-Mumford regularity, thus advancing understanding of hypergraph-associated monomial ideals.

Contribution

It defines inclusion ideals for uniformly increasing hypergraphs and analyzes their algebraic properties, including an upper bound on the regularity of their dual ideals.

Findings

Established algebraic properties of inclusion ideals.

Provided an upper bound for the regularity of the dual ideal.

Enhanced understanding of monomial ideals associated with hypergraphs.

Abstract

In this paper,we introduce the monomial ideals I(H) associated to a special class of non uniform hypergraphs H(X; E; d) namely uniformly increasing hypergraphs. These ideals are named as inclusion ideals. In this paper, we discuss some algebraic properties of these inclusion ideals. In particular, we give an upper bound of the Castlenouvo-Mumford regularity of the special dual ideal I^[*](H) of the inclusion ideal.