Name
Abstract | ||
|---|---|---|
The Riemann–Roch theorem on a graph is related to Alexander duality in combinatorial commutative algebra. We study the lattice ideal given by chip firing on and the initial ideal whose standard monomials are the -parking functions. When is a saturated graph, these ideals are generic and the Scarf complex is a minimal free resolution. Otherwise, syzygies are obtained by degeneration. We also develop a self-contained Riemann–Roch theory for Artinian monomial ideals. |
Year | DOI | Venue |
|---|---|---|
2012 | https://doi.org/10.1007/s10801-012-0386-9 | Journal of Algebraic Combinatorics |
Keywords | Field | DocType |
Riemann–Roch theory for graphs,Combinatorial commutative algebra,Chip firing games,Laplacian matrix of a graph,Lattice ideals and their Betti numbers,Alexander duality of monomial ideals,Scarf complex | Graph,Combinatorics,Lattice (order),Riemann hypothesis,Monomial,Mathematics,Alexander duality,Combinatorial commutative algebra | Journal |
Volume | Issue | ISSN |
37 | 4 | 0925-9899 |
Citations | PageRank | References |
3 | 0.60 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Madhusudan Manjunath | 1 | 31 | 3.58 |
| Bernd Sturmfels | 2 | 926 | 136.85 |