S-functions and characters of Lie algebras and Lie groups
Shifted set families, degree sequences, and plethysm.
Shuffle bialgebras
The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive elements...
Signed words and permutations. II: The Euler-Mahonian polynomials.
Signed words and permutations. III: The MacMahon Verfahren.
Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph
Harary [10, p. 7] claims that Veblen [20, p. 2] first suggested to formalize simple graphs using simplicial complexes. We have developed basic terminology for simple graphs as at most 1-dimensional complexes. We formalize this new setting and then reprove Mycielski’s [12] construction resulting in a triangle-free graph with arbitrarily large chromatic number. A different formalization of similar material is in [15].
Singular eigenfunctions of Calogero-Sutherland type systems and how to transform them into regular ones.
Singularités génériques des variétés de Schubert covexillaires
On montre que les composantes irréductibles du lieu singulier d’une variété de Schubert dans associée à une permutation covexillaire, sont paramétrées par certains des points coessentiels du graphe de la permutation. On donne une description explicite de ces composantes et l’on décrit la singularité le long de chacune d’entre elles.
Skew divided difference operators and Schubert polynomials.
Skew-symmetric cluster algebras of finite mutation type
In the famous paper [FZ2] Fomin and Zelevinsky obtained Cartan-Killing type classification of all cluster algebras of finite type, i.e. cluster algebras having only finitely many distinct cluster variables. A wider class of cluster algebras is formed by cluster algebras of finite mutation type which have finitely many exchange matrices (but are allowed to have infinitely many cluster variables). In this paper we classify all cluster algebras of finite mutation type with skew-symmetric exchange matrices....
Sklyanin determinant for reflection algebra.
Small bases for finite groups
Small integral trees.
Some applications of the proper and adjacency polynomials in the theory of graph spectra.
Some bijective correspondences involving domino tableaux.
Some classical expansions for Knop-Sahi and Macdonald polynomials.
Some design theoretic results on the Conway group .0.
Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes.
Some new methods in the theory of -quasi-invariants.
Some plethysm results related to Foulkes' conjecture.