Generalized -Newton inequalities revisited.
Generating functions for statistics on .
Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables.
Hall-Littlewood functions and Kostka-Foulkes polynomials in representation theory.
Hook lengths in a skew Young diagram.
Hopf algebras and dendriform structures arising from parking functions
We introduce a graded Hopf algebra based on the set of parking functions (hence of dimension in degree n). This algebra can be embedded into a noncommutative polynomial algebra in infinitely many variables. We determine its structure, and show that it admits natural quotients and subalgebras whose graded components have dimensions respectively given by the Schröder numbers (plane trees), the Catalan numbers, and powers of 3. These smaller algebras are always bialgebras and belong to some family...
Hyperoctahedral species.
Hypersymmetric functions and Pochhammers of nonautonomous matrices.
Ideals and quotients of -quasisymmetric polynomials.
Inequalities related to rearrangements of powers and symmetric polynomials.
Integrality of two variable Kostka functions.
Intertwining Operators and Polynomials Associated with the Symmetric Group.
Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables.
Jucys-Murphy elements and the unitary Weingarten function
We describe an approach to the unitary Weingarten function based on the JM elements of symmetric group algebras. When combined with previously known properties of the Weingarten function, this gives a surprising connection with the Moebius function of the lattice of noncrossing partitions.
Keys and alternating sign matrices.
Kronecker product identities from D-finite symmetric functions.
Lattice path proofs of extended Bressoud-Wei and Koike skew Schur function identities.
Le module dendriforme sur le groupe cyclique
La structure d’opérade anticyclique de l’opérade dendriforme donne en particulier une matrice d’ordre agissant sur l’espace engendré par les arbres binaires plans à feuilles. On calcule le polynôme caractéristique de cette matrice. On propose aussi une conjecture compatible pour le polynôme caractéristique de la transformation de Coxeter du poset de Tamari, qui est essentiellement une racine carrée de cette matrice.
Linearly independent products of rectangularly complementary Schur functions.
Littlewood-Richardson coefficients and integrable tilings.