Combinatorial Models for the Finite-Dimensional Grassmannians.
Combinatorial topology and the global dimension of algebras arising in combinatorics
In a highly influential paper, Bidigare, Hanlon and Rockmore showed that a number of popular Markov chains are random walks on the faces of a hyperplane arrangement. Their analysis of these Markov chains took advantage of the monoid structure on the set of faces. This theory was later extended by Brown to a larger class of monoids called left regular bands. In both cases, the representation theory of these monoids played a prominent role. In particular, it was used to compute the spectrum of the...
Compact packings in the Euclidean space
Compatible complex structures on twistor space
Let be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space admits a natural metric. The aim of this article is to study properties of complex structures on which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space .
Complex Hadamard matrices and the spectral set conjecture.
By analyzing the connection between complex Hadamard matrices and spectral sets, we prove the direction "spectral ⇒ tile" of the Spectral Set Conjecture, for all sets A of size |A| ≤ 5, in any finite Abelian group. This result is then extended to the infinite grid Zd for any dimension d, and finally to Rd.
Computer Generated Islamic Star Patterns
Computing parametric rational generating functions with a primal Barvinok algorithm.
Computing the period of an Ehrhart quasi-polynomial.
Configuration spaces of weighted graphs in high dimensional Euclidean spaces.
Conformally symmetric circle packings: A generalization of Doyle's spirals.
Conjecturally optimal coverings of an equilateral triangle with up to 36 equal circles.
Constructing subsets of a given packing index in Abelian groups
Construction of minimal bracketing covers for rectangles.
Convex bodies associated to linear series
In his work on log-concavity of multiplicities, Okounkov showed in passing that one could associate a convex body to a linear series on a projective variety, and then use convex geometry to study such linear systems. Although Okounkov was essentially working in the classical setting of ample line bundles, it turns out that the construction goes through for an arbitrary big divisor. Moreover, this viewpoint renders transparent many basic facts about asymptotic invariants of linear series, and opens...
Convex Disks Can Cover Their Shadow.
Convex Polyhedra With Triangular Faces and Cone Triangulation
Convexity in subsets of lattices.
The notion of convex set for subsets of lattices in one particular case was introduced in [1], where it was used to study Paretto's principle in the theory of group choice. This notion is based on a betweenness relation due to Glivenko [2]. Betweenness is used very widely in lattice theory as basis for lattice geometry (see [3], and, especially [4 part 1]).In the present paper the relative notions of convexity are considered for subsets of an arbitrary lattice.In section 1 certain relative notions...
Convexly independent subsets of the Minkowski sum of planar point sets.
Correction to the paper: Packing of 180 equal circles on a sphere. Elemente der Mathematik. Vol. 38, 1983, 119-122.
Countable Decompositions of R2 and R3 .