Combinatorial Commutative Algebra (Graduate Texts in Mathematics, Volume 227)
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Contents:
Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied Graduate Texts in Mathematics. Combinatorial commutative algebra is a broad area of mathematics, and one can material can be found in the proceedings volumes [EGM98] and [AGHSS04].
Abstract We study minimal free resolutions of edge ideals of bipartite graphs. We associate a directed graph to a bipartite graph whose edge ideal is unmixed, and give expressions for the regularity and the depth of the edge ideal in terms of invariants of the directed graph. For some classes of unmixed edge ideals, we show that the arithmetic rank of the ideal equals projective dimension of its quotient.
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Evans ; B. Uhler : Commuting birth-and-death processes. The annals of applied probability , 20 1 , p. Nie ; K.
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Sturmfels : The algebraic degree of semidefinite programming. Rostalski and B. Sturmfels : Dualities in convex algebraic geometry. Rendiconti di matematica e delle sue applicazioni , 30 , p. Shiu and B. Sturmfels : Siphons in chemical reaction networks. Bulletin of mathematical biology , 72 6 , p. Uhler : Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry.
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