By Anne Schilling
This ebook offers an advent to the very energetic box of combinatorics of affine Schubert calculus, explains the present cutting-edge, and states the present open difficulties. Affine Schubert calculus lies on the crossroads of combinatorics, geometry, and illustration idea. Its glossy improvement is influenced by means of likely unrelated instructions. One is the advent of k-Schur capabilities within the learn of Macdonald polynomial positivity, a more often than not combinatorial department of symmetric functionality idea. the opposite path is the research of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formula of an issue in enumerative geometry.
This is the 1st introductory textual content in this topic. It comprises many examples in Sage, a loose open resource common function mathematical software program procedure, to attract the reader to enquire the open difficulties. This e-book is written for complex undergraduate and graduate scholars, in addition to researchers, who are looking to familiarize yourself with this interesting new field.
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