A constructive approach to minimal free resolutions of path ideals of trees

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Rachelle R. Bouchat¹  Tricia Muldoon Brown² 

[1] Indiana University of Pennsylvania;Armstrong State University

关键词: Betti numbers;    Path ideals;    Rooted trees;    Monomial ideals;   

DOI  :  10.13069/jacodesmath.63088

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

For a rooted tree Γ, we consider path ideals of Γ, which are ideals that are generated by all directedpaths of a fixed length in Γ. In this paper, we provide a combinatorial description of the minimalfree resolution of these path ideals. In particular, we provide a class of subforests of Γ that are inone-to-one correspondence with the multi-graded Betti numbers of the path ideal as well as providinga method for determining the projective dimension and the Castelnuovo-Mumford regularity of agiven path ideal.

【 授权许可】

CC BY