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

#### Rachelle R. BOUCHAT [1] , Tricia Muldoon BROWN [2]

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.
Betti numbers, Path ideals, Rooted trees, Monomial ideals
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Subjects Engineering Articles Author: Rachelle R. BOUCHAT Author: Tricia Muldoon BROWN Publication Date : January 11, 2017
 Bibtex @research article { jacodesmath284553, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2017}, volume = {4}, pages = {23 - 35}, doi = {10.13069/jacodesmath.63088}, title = {A constructive approach to minimal free resolutions of path ideals of trees}, key = {cite}, author = {Bouchat, Rachelle R. and Brown, Tricia Muldoon} } APA Bouchat, R , Brown, T . (2017). A constructive approach to minimal free resolutions of path ideals of trees . Journal of Algebra Combinatorics Discrete Structures and Applications , 4 (1) , 23-35 . DOI: 10.13069/jacodesmath.63088 MLA Bouchat, R , Brown, T . "A constructive approach to minimal free resolutions of path ideals of trees" . Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 23-35 Chicago Bouchat, R , Brown, T . "A constructive approach to minimal free resolutions of path ideals of trees". Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 23-35 RIS TY - JOUR T1 - A constructive approach to minimal free resolutions of path ideals of trees AU - Rachelle R. Bouchat , Tricia Muldoon Brown Y1 - 2017 PY - 2017 N1 - doi: 10.13069/jacodesmath.63088 DO - 10.13069/jacodesmath.63088 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 23 EP - 35 VL - 4 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.63088 UR - https://doi.org/10.13069/jacodesmath.63088 Y2 - 2020 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications A constructive approach to minimal free resolutions of path ideals of trees %A Rachelle R. Bouchat , Tricia Muldoon Brown %T A constructive approach to minimal free resolutions of path ideals of trees %D 2017 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 4 %N 1 %R doi: 10.13069/jacodesmath.63088 %U 10.13069/jacodesmath.63088 ISNAD Bouchat, Rachelle R. , Brown, Tricia Muldoon . "A constructive approach to minimal free resolutions of path ideals of trees". Journal of Algebra Combinatorics Discrete Structures and Applications 4 / 1 (January 2017): 23-35 . https://doi.org/10.13069/jacodesmath.63088 AMA Bouchat R , Brown T . A constructive approach to minimal free resolutions of path ideals of trees. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(1): 23-35. Vancouver Bouchat R , Brown T . A constructive approach to minimal free resolutions of path ideals of trees. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(1): 23-35.

Authors of the Article
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