Combinatorial Commutative Algebra

By Ezra Miller, Bernd Sturmfels. 2004

1,574 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9ab4a8bbfe56edb23a98564c8df3514e46d62530

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Citations in the corpus

A Gröbner basis for Kazhdan-Lusztig ideals (2009, methodology): “We now use some notions from combinatorial commutative algebra which can be found in the textbook [MilStu05].”
PRIMER FOR THE ALGEBRAIC GEOMETRY OF SANDPILES (2011, neutral): “Our reference for this section is [22].”
Symbolic Powers and Matroids (2010, background): “ll we deﬁne the basic objects involved in the statem ent. For the part concerning commutative algebra and Stanley-Reisner rings, we refer toBruns and Herzog [BH], Stanley [St] or Miller and Sturmfels [MS]. For what concerns the theory of matroids, some references are the book of Welsh [We] or that o”
Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers (2006, background): “nomial ideals I⊆ R= k[x 1,...,xn] ˙ we are in fact studying a fundamental problem in commutative algebra which asks for the minimal graded free resolution of a monomial ideal (for an introduction see [24]). The edge ideal approach 2000 Mathematics Subject Classiﬁcation. 13D40, 13D02, 05C90, 05E99. K”
Monomial and toric ideals associated to Ferrers graphs (2006, methodology): “Our description of the free resolution of a Ferrers ideal relies on the theory of cellular resolutions as developed by Bayer and Sturmfels in [3] (see also [42]).”
Regularity of Squarefree Monomial Ideals (2013, neutral): “We follow standard texts [3, 30, 39, 45] in these fields.”
On the shape of a pure O-sequence (2010, background): “The characterization of these is also unknown (see some of the standard texts on the subject, such as [58, 66], and the results mentioned below).”
Grobner Bases in Commutative Algebra (2011, background): “Instead, one of the main goals of this last chapter of this monograph is to inspire and to enable the reader, who is interested in further developments and other aspects of the theory, to read more advanced monographs and articles on these subjects, for example, the monograph of Sturmfels [St95] whi”