The weak Lefschetz properties of artinian monomial algebras associated to certain tadpole graphs

Phan Minh Hung; Nguyen Duy Phuoc; Tran Nguyen Thanh Son

The weak Lefschetz properties of artinian monomial algebras associated to certain tadpole graphs

Commutative Algebra 2024-12-12 v1 Combinatorics

Authors: Phan Minh Hung , Nguyen Duy Phuoc , Tran Nguyen Thanh Son

Abstract

Given a simple graph $G$ , the artinian monomial algebra associated to $G$ , denoted by $A(G)$ , is defined by the edge ideal of $G$ and the squares of the variables. In this article, we classify some tadpole graphs $G$ for which $A(G)$ has or fails the weak Lefschetz property.

Keywords

graph representation learning heterogeneous graphs large language models feature alignment GNN

Cite

@article{arxiv.2412.08037,
  title  = {The weak Lefschetz properties of artinian monomial algebras associated to certain tadpole graphs},
  author = {Phan Minh Hung and Nguyen Duy Phuoc and Tran Nguyen Thanh Son},
  journal= {arXiv preprint arXiv:2412.08037},
  year   = {2024}
}

Comments

12 pages. arXiv admin note: substantial text overlap with arXiv:2310.14368 by other authors

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