This article grew out of a complicated 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 matters. The e-book is split into 3 chapters. the 1st is dedicated to symmetric features and particularly to Schur polynomials. those are polynomials with optimistic 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 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 delicate connections among difficulties of enumeration of diminished 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 forms, subvarieties of Grassmannians, and flag types outlined by way of convinced occurrence stipulations with mounted subspaces. This quantity makes obtainable a few effects, making a good stepping stone for scaling extra formidable heights within the zone. The author's purpose used to be to stay basic: the 1st chapters require no past wisdom, the 3rd bankruptcy makes use of a few rudimentary notions of topology and algebraic geometry. hence, a entire appendix at the topology of algebraic kinds is equipped. This e-book is the English translation of a textual content formerly released in French.
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