Classification of unilateral and equitransitive tilings by squares pf three sizes.
Closures of faces of compact convex sets
This paper gives necessary and sufficient conditions for the closure of a face in a compact convex set to be again a face. As applications of these results, several theorems scattered in the literature are proved in an economical and uniform manner.
Clusters minimizing area plus length of singular curves.
Coating by cubes.
Cochain operations and subspace arrangements.
Cognition: Differential-geometrical view on neural networks.
Colored partitions and a generalization of the braid arrangement.
Colouring Platonic Solids
Combinatorial 3-manifolds with 10 vertices.
Combinatorial Complexity Bounds for Arrangements of Curves and Spheres.
Combinatorial construction of toric residues.
In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated polytopes are essential. We reduce the problem to finding a collection of partitions of the lattice points in the polytopes satisfying a certain combinatorial property. We use this description to solve the problem when and for any when the polytopes of the divisors share a complete flag of faces. The latter generalizes earlier...
Combinatorial d-Tori with a Large Symmetry Group.
Combinatorial fans, lattice-ordered groups, and their neighbours: A short excursion.
Combinatorial formulae for multiple set-valued labellings.
Combinatorial lemmas for polyhedrons
We formulate general boundary conditions for a labelling to assure the existence of a balanced n-simplex in a triangulated polyhedron. Furthermore we prove a Knaster-Kuratowski-Mazurkiewicz type theorem for polyhedrons and generalize some theorems of Ichiishi and Idzik. We also formulate a necessary condition for a continuous function defined on a polyhedron to be an onto function.
Combinatorial lemmas for polyhedrons I
We formulate general boundary conditions for a labelling of vertices of a triangulation of a polyhedron by vectors to assure the existence of a balanced simplex. The condition is not for each vertex separately, but for a set of vertices of each boundary simplex. This allows us to formulate a theorem, which is more general than the Sperner lemma and theorems of Shapley; Idzik and Junosza-Szaniawski; van der Laan, Talman and Yang. A generalization of the Poincaré-Miranda theorem is also derived.
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...
Combinatorial-geometric aspects of polycategory theory : pasting schemes and higher Bruhat orders (list of results)
Common supporting lines for families of convex bodies in the plane.