This article grew out of a sophisticated path taught via the writer on the Fourier Institute (Grenoble, France). It serves as an creation to the combinatorics of symmetric features, extra accurately to Schur and Schubert polynomials. additionally studied is the geometry of Grassmannians, flag kinds, and particularly, their Schubert types. This e-book examines profound connections that unite those topics. The ebook is split into 3 chapters. the 1st is dedicated to symmetric capabilities and particularly to Schur polynomials. those are polynomials with confident integer coefficients within which all of the monomials correspond to a tender tableau with the valuables of being 'semistandard'. the second one bankruptcy is dedicated to Schubert polynomials, which have been found via A. Lascoux and M. P. Schutzenberger who deeply probed their combinatorial properties.It is proven, for instance, that those polynomials help the delicate connections among difficulties of enumeration of decreased decompositions of diversifications and the Littlewood-Richardson rule, a very efficacious model of that may be derived from those connections. the ultimate bankruptcy is geometric. it really is dedicated to Schubert forms, subvarieties of Grassmannians, and flag kinds outlined by way of sure prevalence stipulations with mounted subspaces. This quantity makes available a few effects, making a good stepping stone for scaling extra formidable heights within the zone. The author's cause was once to stay common: the 1st chapters require no previous wisdom, the 3rd bankruptcy makes use of a few rudimentary notions of topology and algebraic geometry. consequently, a complete appendix at the topology of algebraic types is equipped. This ebook is the English translation of a textual content formerly released in French.
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