This article grew out of a complicated path taught by way of the writer on the Fourier Institute (Grenoble, France). It serves as an advent to the combinatorics of symmetric features, extra accurately to Schur and Schubert polynomials. additionally studied is the geometry of Grassmannians, flag forms, and particularly, their Schubert kinds. This ebook examines profound connections that unite those matters. The booklet is split into 3 chapters. the 1st is dedicated to symmetric services and particularly to Schur polynomials. those are polynomials with confident integer coefficients during 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, that have been chanced on by means of A. Lascoux and M. P. Schutzenberger who deeply probed their combinatorial properties.It is proven, for instance, that those polynomials help the sophisticated connections among difficulties of enumeration of decreased decompositions of variations and the Littlewood-Richardson rule, a very efficacious model of that could be derived from those connections. the ultimate bankruptcy is geometric. it truly is dedicated to Schubert types, subvarieties of Grassmannians, and flag kinds outlined via convinced prevalence stipulations with fastened subspaces. This quantity makes obtainable a couple of effects, making a good stepping stone for scaling extra bold heights within the quarter. The author's rationale used to be to stay simple: the 1st chapters require no past wisdom, the 3rd bankruptcy makes use of a few rudimentary notions of topology and algebraic geometry. therefore, a entire appendix at the topology of algebraic forms is supplied. This e-book is the English translation of a textual content formerly released in French.
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