A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin.
A cluster expansion formula ( case).
A combinatorial bijection between standard Young tableaux and reduced words of Grassmannian permutations.
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 Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties.
A Little bijection for affine Stanley symmetric functions.
A note on exponents vs root heights for complex simple Lie algebras.
A -analogue of a formula of Frobenius.
A Pieri-type formula for even orthogonal Grassmannians
We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions of "barred...
A Pieri-type theorem for Lagrangian and odd Orthogonal Grassmannians.
A quantitative aspect of non-unique factorizations: the Narkiewicz constants II
Let K be an algebraic number field with non-trivial class group G and be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let denote the number of non-zero principal ideals with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that behaves, for x → ∞, asymptotically like . In this article, it is proved that for every prime p, , and it is also proved that if and m is large enough. In particular, it is shown that for...
A two-dimensional pictorial presentation of Berele's insertion algorithm for symplectic tableaux.
Advanced determinant calculus.
Algebraic combinatorics related to the free Lie algebra.
An improved tableau criterion for Bruhat order.
Asymptotics for random walks in alcoves of affine Weyl groups.
Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Plücker relations.
Boolean differential operators
We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.
Bruhat intervals, polyhedral cones and Kazhdan-Lusztig-Stanley polynomials.