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TitleMonomials, binomials and Riemann-Roch.
Author(s) Madhusudan Manjunath, Bernd Sturmfels
TypeArticle in Journal
AbstractThe Riemann–Roch theorem on a graph G is related to Alexander duality in combinatorial commutative algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When G 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.
KeywordsRiemann–Roch theory for graphs, Combinatorial commutative algebra, Chip firing games, Laplacian matrix of a graph, Lattice ideals and their Betti numbers
ISSN0925-9899; 1572-9192/e
URL http://link.springer.com/article/10.1007%2Fs10801-012-0386-9
LanguageEnglish
JournalJ. Algebr. Comb.
Volume37
Number4
Pages737--756
PublisherSpringer US, New York, NY
Year2013
Edition0
Translation No
Refereed No
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