Schubert and Grothendieck: a bidecennial balance. (Schubert et Grothendieck: un bilan bidécennal.)
Schubert functions and the number of reduced words of permutations.
Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces
The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.
Schur functions and alternating sums.
Schur functions: Theme and variations.
Schur -functions and spin characters of symmetric groups. I.
Schur-convexity of the complete elementary symmetric function.
Semicanonical basis generators of the cluster algebra of type .
Semistandard matrices and tableaux. (Matrices et tableaux semi-standard.)
Separability number and Schurity number of coherent configurations.
Séries de croissance et polynômes d'Ehrhart associés aux réseaux de racines
Étant donnés un système de racines d’une des familles A, B, C, D, F, G et le groupe abélien libre qu’il engendre, on calcule explicitement la série de croissance de ce groupe relativement à Les résultats s’interprètent en termes du polynôme d’Ehrhart de l’enveloppe convexe de .
Set-polynomials and polynomial extension of the Hales-Jewett theorem.
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.