Minimal free resolutions of lattice ideals of digraphs
Algebraic Combinatorics, Volume 1 (2018) no. 2, pp. 283-326.

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.

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DOI: 10.5802/alco.15
Classification: 13D02,  13P10,  05C25,  05C50,  05EXX
Keywords: Directed graph, lattice ideal, Gröbner basis, minimal free resolution
O’Carroll, Liam 1; Planas-Vilanova, Francesc 2

1 School of Mathematics University of Edinburgh James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD Scotland.
2 Departament de Matemàtiques ETSEIB, Universitat Politècnica de Catalunya Diagonal 647, ETSEIB, 08028 Barcelona Catalunya.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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. https://alco.centre-mersenne.org/articles/10.5802/alco.15/

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