The weak Lefschetz property for monomial ideals of small type

JOURNAL OF ALGEBRA

卷:462

Article

Ii, David Cook¹  Nagel, Uwe² 

[1] Eastern Illinois Univ, Dept Math & Comp Sci, Charleston, IL 61920 USA

[2] Univ Kentucky, Dept Math, 715 Patterson Off Tower, Lexington, KY 40506 USA

关键词: Monomial ideals;    Weak Lefschetz property;    Determinants;    Lozenge tilings;    Non-intersecting lattice paths;    Perfect matchings;    Enumeration;   

DOI  :  10.1016/j.jalgebra.2016.06.004

来源: Elsevier

【 摘 要 】

In this work a combinatorial approach towards the weak Lefschetz property is developed that relates this property to enumerations of signed perfect matchings as well as to enumerations of signed families of non-intersecting lattice paths in certain triangular regions. This connection is used to study Artinian quotients by monomial ideals of a three-dimensional polynomial ring. Extending a main result in the recent memoir [1], we completely classify the quotients of type two that have the weak Lefschetz property in characteristic zero. We also derive results in positive characteristic for quotients whose type is at most two. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free