The Apollonian decay of beer foam bubble size distribution and the lattices of Young diagrams and their correlated mixing functions.
The combinatorics of Macdonald's operator.
The combinatorics of orbital varieties closures of nilpotent order 2 in .
The combinatorics of quiver representations
We give a description of faces, of all codimensions, for the cones spanned by the set of weights associated to the rings of semi-invariants of quivers. For a triple flag quiver and its faces of codimension 1 this description reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone. We give new applications to Littlewood-Richardson coefficients, including a product formula for LR-coefficients corresponding to triples of partitions lying on a wall of the Klyachko cone. We systematically...
The combinatorics of the Garsia-Haiman modules for hook shapes.
The exact asymptotic of the time to collision.
The Garnir relations for Weyl groups of type .
The hive model and the factorisation of Kostka coefficients.
The hive model and the polynomial nature of stretched Littlewood-Richardson coefficients.
The hook fusion procedure.
The integer sequence A002620 and upper antagonistic functions.
The Littlewood-Richardson rule - the cornerstone for computing group properties
The major counting of nonintersecting lattice paths and generating functions for tableaux. (Summary).
The number of complete exceptional sequences for a Dynkin algebra
The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper determines the number of complete exceptional sequences for any Dynkin algebra. Since the complete exceptional sequences for a Dynkin algebra of Dynkin type Δ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type Δ, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.
The permutation classes equinumerous to the smooth class.
The plethysm at hook and near-hook shapes.
The product of trees in the Loday-Ronco algebra through Catalan alternative tableaux.
The ring of multisymmetric functions
We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring , thereby answering a classical question coming from works of F. Junker [J1, J2, J3] in the late nineteen century and then implicitly in H. Weyl book “The classical groups” [W].
The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at .
The skeleton of a reduced word and a correspondence of Edelman and Green.