A Broken Circuit Ring
By Nicholas Proudfoot, David E. Speyer. 2004
92 citations recorded by the source corpus.
Given a matroid M represented by a linear subspace L in n-space (equivalently by an arrangement of n hyperplanes in L), we define a graded ring R(L) which degenerates to the Stanley-Reisner ring of the broken circuit complex for any choice of ordering of the ground set. In particular, R(L) is Cohen-Macaulay, and may be used to compute the h-vector of the broken circuit complex of M. We give a geometric interpretation of Spec R(L), as well as a stratification indexed by the flats of M.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/bc02cc1ad8d0f38ecbcdb39882d9c4bc88880d82
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Federico Ardila
- Alexander Postnikov
- Bernd Sturmfels
- Caroline Uhler
- Nicholas Proudfoot
- Eric Katz
- Jenia Tevelev
- M. Develin
In Computational Theory and Mathematics
- Federico Ardila
- Bernd Sturmfels
- Caroline Uhler
- Alexander Postnikov
- Nicholas Proudfoot
- Eric Katz
- David E. Speyer
- Martyn Marshall
In Discrete Mathematics and Combinatorics
- Federico Ardila
- Bernd Sturmfels
- Alexander Postnikov
- Caroline Uhler
- Nicholas Proudfoot
- Lauren K. Williams
- David E. Speyer
- Thomas Lam
Citations in the corpus
- Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry (2009, background): “For experts in combinatorial commutative algebra, we note that Proudfoot and Speyer (2006) actually prove the following stronger results.”
- A survey of hypertoric geometry and topology (2007, background): “of φ, and in fact I(A) is generated by such elements. Since kS is clearly homogeneous, R(A) is a graded ring, with the usual convention of degei = 2 for all i. 14 The following proposition, proven in [PS, 4], states that the ring R(A) is a simultaneous deformation of the various Stanley-Reisner ring”
- Combinatorics and geometry of power ideals (2008, background): “• (Berget [4], Brion-Verge [5], Orlik-Terao [13], Proudfoot-Speyer [17], Terao [23]) Given a hyperplane arrangement determined by the linear functionals α1, . . . , αn, various subalgebras of the algebra generated by 1α1 , . . . , 1 αn have been studied, in some cases with additional structure.”