Combinatorial aspects of polylogarithms and Euler-Zagier sums. (Aspects combinatoires des polylogarithmes et des sommes d'Euler-Zagier.)
Combinatorial constructions of weight bases: the Gelfand-Tsetlin basis.
Combinatorial interpretations for rank-two cluster algebras of affine type.
Combinatorial Laplacian of the matching complex.
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 operators for Kronecker powers of representations of .
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 vs. algebraic characterizations of completely pseudo-regular codes.
Combinatorics, superalgebras, invariant theory and representation theory.
Completeness conditions in certain Weyl complexes, combinatorics and parsimony.
Complex Hadamard Matrices contained in a Bose–Mesner algebra
Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric...
Composition of transpositions and equality of ribbon Schur -functions.
Computing and proving with pivots
A simple idea used in many combinatorial algorithms is the idea of pivoting. Originally, it comes from the method proposed by Gauss in the 19th century for solving systems of linear equations. This method had been extended in 1947 by Dantzig for the famous simplex algorithm used for solving linear programs. From since, a pivoting algorithm is a method exploring subsets of a ground set and going from one subset σ to a new one σ′ by deleting an element inside σ and adding an element outside σ: σ′ = σv} ∪ {u},...
Computing Kazhdan-Lusztig polynomials for arbitrary Coxeter groups.
Computing powers of two generalizations of the logarithm.
Comultiplication rules for the double Schur functions and Cauchy identities.
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.