Conjectured combinatorial models for the Hilbert series of generalized diagonal harmonic modules.
Conjectured statistics for the higher -Catalan sequences.
Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs
The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity. We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.
Construction of extended Steiner systems for information retrieval.
Construction of Mendelsohn designs by using quasigroups of -varieties
Let be a positive integer. An algebra is said to have the property if all of its subalgebras generated by two distinct elements have exactly elements. A variety of algebras is a variety with the property if every member of has the property . Such varieties exist only in the case of prime power. By taking the universes of the subalgebras of any finite algebra of a variety with the property , , blocks of Steiner system of type are obtained. The stated correspondence between Steiner...
Constructions of representations of rank two semisimple Lie algebras with distributive lattices.
Convex-ear decompositions and the flag -vector.
Correspondences between the different types of bijections between the symmetric group and the valued Motzkin paths. (Correspondances entre les différents types de bijections entre le groupe symétrique et les chemins de Motzkin valués.)
Cospectral graphs on 12 vertices.
Counting Young tableaux of bounded height.
Coxeter polynomials of Salem trees
We compute the Coxeter polynomial of a family of Salem trees, and also the limit of the spectral radii of their Coxeter transformations as the number of their vertices tends to infinity. We also prove that if z is a root of multiplicities for the Coxeter polynomials of the trees respectively, then z is a root for the Coxeter polynomial of their join, of multiplicity at least where .
Coxeter-like complexes.
Criteria for shellable multicomplexes.
Crooked functions, bent functions, and distance regular graphs.
Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
We define the -restriction and -induction functors on the category of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.
Cubical convex ear decompositions.
Cyclic sieving for longest reduced words in the hyperoctahedral group.
Decomposition of the diagonal action of on the coinvariant space of .
Determinantal expression and recursion for Jack polynomials.
Determinantal transition kernels for some interacting particles on the line
We find the transition kernels for four markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin–McGregor-type kernel. The resulting kernels all inherit the determinantal structure from the Karlin–McGregor formula, and have a similar form to Schütz’s kernel for the totally asymmetric simple exclusion process.