Combinatorial Laplacian of the matching complex.
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 necklace splitting.
Combinatorial Nullstellensatz approach to polynomial expansion
Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of |f(A,B)| for finite subsets A, B of a field, and a polynomial f(x,y) of the form f(x,y) = g(x) + yh(x), where the degree of g is greater than that of h.
Combinatorial Obstructions to the Lifting of Weaving Diagrams.
Combinatorial operators for Kronecker powers of representations of .
Combinatorial polarization, code loops, and codes of high level.
Combinatorial problems related to geometrically distributed random variables.
Combinatorial proof of a curious -binomial coefficient identity.
Combinatorial proofs of Capelli's and Turnbull's identities from classical invariant theory.
Combinatorial proofs of some Simons-type binomial coefficient identities.
Combinatorial properties of Fourier-Motzkin elimination.
Combinatorial properties of one-dimensional arrangements.
Combinatorial properties of products of graphs
Combinatorial properties of the antichains of a Garland.
Combinatorial results for semigroups of order-decreasing partial transformations.
Combinatorial stacks and the four-color theorem
Combinatorial statistics on type-B analogues of noncrossing partitions and restricted permutations.