A conjecture of Biggs concerning the resistance of a distance-regular graph.
A decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth algorithm.
A Deformed Quon Algebra
The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators , , on an infinite dimensional vector space satisfying the...
A derivation of Kohnert's algorithm from Monk's rule.
A direct bijective proof of the hook-length formula.
A family of tridiagonal pairs related to the quantum affine algebra .
A four-class association scheme derived from a hyperbolic quadric in .
A Frobenius formula for the characters of the Hecke algebras.
A generalization of an inequality involving the generalized elementary symmetric mean.
A generalization of combinatorial Nullstellensatz.
A generalization of Jaeger-Nomura's Bose Mesner algebra associated to type II matrices
A category generalizing Jaeger-Nomura algebra associated to a spin model is given. It is used to prove some equivalence among the four conditions by Jaeger-Nomura for spin models of index 2.
A generalized major index statistic.
A geometric version of the Kerov-Kirillov-Reshetikhin construction. (Une version géométrique de la construction de Kerov-Kirilov-Reshetikhin.)
A graph-theoretic method for choosing a spanning set for a finite-dimensional vector space, with applications to the Grossman-Larson-Wright module and the Jacobian conjecture.
A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties.
A Little bijection for affine Stanley symmetric functions.
A Littlewood-Richardson rule for evaluation representations of .
A Macdonald vertex operator and standard tableaux statistics for the two-column -Kosta coefficients.
A matrix representation of graphs and its spectrum as a graph invariant.
A minimal Set of Generators for the Ring of multisymmetric Functions
The purpose of this article is to give, for any (commutative) ring , an explicit minimal set of generators for the ring of multisymmetric functions as an -algebra. In characteristic zero, i.e. when is a -algebra, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving the degree bound previously...