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We prove a Matrix-Tree Theorem enumerating the spanning trees of a cell complex in terms of the eigenvalues of its cellular Laplacian operators, generalizing a previous result for simplicialâ€¦ (More)

- Federico Ardila, Caroline J. Klivans
- J. Comb. Theory, Ser. B
- 2006

We study the Bergman complex B(M) of a matroid M: a polyhedral complex which arises in algebraic geometry, but which we describe purely combinatorially. We prove that a natural subdivision of theâ€¦ (More)

We generalize the definition and enumeration of spanning trees from the setting of graphs to that of arbitrary-dimensional simplicial complexes âˆ†, extending an idea due to G. Kalai. We prove aâ€¦ (More)

We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacianâ€¦ (More)

- Caroline J. Klivans, Victor Reiner
- Electr. J. Comb.
- 2008

We study, in three parts, degree sequences of k-families (or k-uniform hypergraphs) and shifted k-families. â€¢ The first part collects for the first time in one place, various implications such asâ€¦ (More)

- Johnny GuzmÃ¡n, Caroline J. Klivans
- J. Comb. Theory, Ser. A
- 2015

We consider chip-firing dynamics defined by arbitrary M-matrices. M-matrices generalize graph Laplacians and were shown by Gabrielov to yield avalanche finite systems. Building on the work of Bakerâ€¦ (More)

- Ronen Basri, Pedro F. Felzenszwalb, Ross B. Girshick, David W. Jacobs, Caroline J. Klivans
- 2009 IEEE Conference on Computer Vision andâ€¦
- 2009

To recognize three-dimensional objects it is important to model how their appearances can change due to changes in viewpoint. A key aspect of this involves understanding which object features can beâ€¦ (More)

We study the class of matroids whose independent set complexes are shifted simplicial complexes. We prove two characterization theorems, one of which is constructive. In addition, we show this classâ€¦ (More)

- Caroline J. Klivans, Ed Swartz
- Discrete & Computational Geometry
- 2011

We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones are given by the coefficients of the characteristic polynomial of the arrangement. Thisâ€¦ (More)

We consider projections of points onto fundamental chambers of finite real reflection groups. Our main result shows that for groups of type An, Bn, and Dn, the coefficients of the characteristicâ€¦ (More)