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.