Based upon a previous work of Manjunath and Sturmfels for a finite, complete, undirected graph, and a refined algorithm by Eröcal, Motsak, Schreyer and Steenpaß for computing syzygies, we display a free resolution of the lattice ideal associated to a finite, strongly connected, weighted, directed graph. Moreover, the resolution is minimal precisely when the digraph is strongly complete.
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.15
Keywords: Directed graph, lattice ideal, Gröbner basis, minimal free resolution
@article{ALCO_2018__1_2_283_0, author = {O{\textquoteright}Carroll, Liam and Planas-Vilanova, Francesc}, title = {Minimal free resolutions of lattice ideals of digraphs}, journal = {Algebraic Combinatorics}, pages = {283--326}, publisher = {MathOA foundation}, volume = {1}, number = {2}, year = {2018}, doi = {10.5802/alco.15}, zbl = {06882343}, mrnumber = {3856526}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/alco.15/} }
TY - JOUR AU - O’Carroll, Liam AU - Planas-Vilanova, Francesc TI - Minimal free resolutions of lattice ideals of digraphs JO - Algebraic Combinatorics PY - 2018 SP - 283 EP - 326 VL - 1 IS - 2 PB - MathOA foundation UR - http://archive.numdam.org/articles/10.5802/alco.15/ DO - 10.5802/alco.15 LA - en ID - ALCO_2018__1_2_283_0 ER -
%0 Journal Article %A O’Carroll, Liam %A Planas-Vilanova, Francesc %T Minimal free resolutions of lattice ideals of digraphs %J Algebraic Combinatorics %D 2018 %P 283-326 %V 1 %N 2 %I MathOA foundation %U http://archive.numdam.org/articles/10.5802/alco.15/ %R 10.5802/alco.15 %G en %F ALCO_2018__1_2_283_0
O’Carroll, Liam; Planas-Vilanova, Francesc. Minimal free resolutions of lattice ideals of digraphs. Algebraic Combinatorics, Volume 1 (2018) no. 2, pp. 283-326. doi : 10.5802/alco.15. http://archive.numdam.org/articles/10.5802/alco.15/
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