@article{article_284553, title={A constructive approach to minimal free resolutions of path ideals of trees}, journal={Journal of Algebra Combinatorics Discrete Structures and Applications}, volume={4}, pages={23–35}, year={2017}, DOI={10.13069/jacodesmath.63088}, author={Bouchat, Rachelle R. and Brown, Tricia Muldoon}, keywords={Betti numbers,Path ideals,Rooted trees,Monomial ideals}, abstract={For a rooted tree $\Gamma ,$ we consider path ideals of $\Gamma$, which are ideals that are generated by all directed paths of a fixed length in $\Gamma$. In this paper, we provide a combinatorial description of the minimal free resolution of these path ideals. In particular, we provide a class of subforests of $\Gamma$ that are in one-to-one correspondence with the multi-graded Betti numbers of the path ideal as well as providing a method for determining the projective dimension and the Castelnuovo-Mumford regularity of a given path ideal.}, number={1}, publisher={iPeak Academy}