Free quasi-symmetric functions, product actions and quantum field theory of partitions.
From a 1-rotational RBIBD to a partitioned difference family.
Further determinant identities related to classical root systems
By introducing polynomials in matrix entries, six determinants are evaluated which may be considered extensions of Vandermonde-like determinants related to the classical root systems.
Gelfand-Graev characters of the finite unitary groups.
Generalization of Waring-type formulas. (Généralisation de formules de type Waring.)
Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups
We construct a subalgebra of dimension of the group algebra of the Weyl group of type containing its usual Solomon algebra and the one of : is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras . Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to . In an appendix, P. Baumann and C. Hohlweg present in an explicit and...
Generalized Dumont-Foata polynomials and alternative tableaux.
Generalized -Newton inequalities revisited.
Generating functions attached to some infinite matrices.
Generating functions for statistics on .
Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories
The homology theory of colored posets, defined by B. Everitt and P. Turner, is generalized. Two graph categories are defined and Khovanov type graph cohomology are interpreted as Ext* groups in functor categories associated to these categories. The connection, described by J. H. Przytycki, between the Hochschild homology of an algebra and the graph cohomology, defined for the same algebra and a cyclic graph, is explained from the point of view of homological algebra in functor categories.
Graphical condensation, overlapping Pfaffians and superpositions of matchings.
Graphical introduction to classical Lie algebras.
Gröbner basis techniques in algebraic combinatorics.
Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables.
-vectors, Eulerian polynomials and stable polytopes of graphs.
Hadamard matrices and strongly regular graphs with the 3-e. c. adjacency property.
Hall-Littlewood functions and Kostka-Foulkes polynomials in representation theory.
Hardness of embedding simplicial complexes in
Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all , with...
Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...