Divisors on graphs, binomial and monomial ideals, and cellular resolutions

Graph;Divisors;Chip-firing;Potential theory;Green's function;Grobner theory;Hyperplane arrangement;Lattice;Delaunay decomposition;Totally unimodular;Polyhedral cellular minimal free resolution

Shokrieh, Farbod ; Baker, Matthew Mathematics Etnyre, John Leykin, Anton Yu, Josephine ; Baker, Matthew

University:Georgia Institute of Technology

Department:Mathematics

关键词: Graph;    Divisors;    Chip-firing;    Potential theory;    Green's function;    Grobner theory;    Hyperplane arrangement;    Lattice;    Delaunay decomposition;    Totally unimodular;    Polyhedral cellular minimal free resolution;   

Others  :  https://smartech.gatech.edu/bitstream/1853/52176/1/SHOKRIEH-DISSERTATION-2013.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs.We use ideas from potential theory on graphs and from the theory of Delaunay decompositions for lattices to describe their minimal polyhedral cellular free resolutions. We show that the resolutions of all these ideals are closely related and that their Z-graded Betti tables coincide.As corollaries, we give conceptual proofs of conjectures and questions posed by Postnikov and Shapiro, by Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various other results related to the theory of chip-firing games on graphs also follow from our general techniques and results.