Canonical characters on quasi-symmetric functions and bivariate Catalan numbers.
Canonical characters on simple graphs
A multiplicative functional on a graded connected Hopf algebra is called the character. Every character decomposes uniquely as a product of an even character and an odd character. We apply the character theory of combinatorial Hopf algebras to the Hopf algebra of simple graphs. We derive explicit formulas for the canonical characters on simple graphs in terms of coefficients of the chromatic symmetric function of a graph and of canonical characters on quasi-symmetric functions. These formulas and...
Character polynomials, their -analogs and the Kronecker product.
Classifying descents according to equivalence .
Colored permutations and skew tableaux. (Permutations colorées et tableaux gauches.)
Colored trees and noncommutative symmetric functions.
Combinatorial Laplacian of the matching complex.
Combinatorial operators for Kronecker powers of representations of .
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.
Construction of extended Steiner systems for information retrieval.