Chip-Firing and Riemann-Roch Theory for Directed Graphs

zbMath1274.05189arXiv1012.0287MaRDI QIDQ2857320

Spencer Backman, Arash Sh. Asadi

Publication date: 1 November 2013

Full work available at URL: https://arxiv.org/abs/1012.0287

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Directed graphs (digraphs), tournaments (05C20) Games on graphs (graph-theoretic aspects) (05C57)

Related Items (14)

Multi-Eulerian tours of directed graphs ⋮ Monomials, binomials and Riemann-Roch ⋮ Minimal free resolutions of lattice ideals of digraphs ⋮ Abelian networks IV. Dynamics of nonhalting networks ⋮ Arithmetical structures on bidents ⋮ Parking functions on nonsingular \(M\)-matrices ⋮ Chip-firing based methods in the Riemann-Roch theory of directed graphs ⋮ Explicit deformation of lattice ideals via chip-firing games on directed graphs ⋮ Chip-Firing Games and Critical Groups ⋮ Chip firing on Dynkin diagrams and McKay quivers ⋮ Chip-firing and energy minimization on M-matrices ⋮ CoEulerian graphs ⋮ A maximizing characteristic for critical configurations of chip-firing games on digraphs ⋮ Chip-firing games on Eulerian digraphs and NP-hardness of computing the rank of a divisor on a graph

Cites Work

• Unnamed Item
• Arithmetical graphs
• Asymmetric Abelian sandpile models
• Riemann-Roch for sub-lattices of the root lattice \(A_n\)
• Riemann-Roch and Abel-Jacobi theory on a finite graph
• Two-Variable Zeta-Functions on Graphs and Riemann–Roch Theorems
• Chip-Firing and Rotor-Routing on Directed Graphs
• Self-organized critical state of sandpile automaton models

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