Diagram Rules for the Generation of Schubert Polynomials
نویسندگان
چکیده
منابع مشابه
Diagram Rules for the Generation of Schubert Polynomials
We prove an elegant combinatorial rule for the generation of Schubert polynomials based on box diagrams, which was conjectured by A. Kohnert. The main tools for the proof are (1) a recursive structure of Schubert polynomials and (2) a partial order on the set of box diagrams. As a byproduct we obtain (combinatorial) proofs for two other rules for the generation of Schubert polynomials based on ...
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The lattice cell in the i + 1 st row and j + 1 st column of the positive quadrant of the plane is denoted i; j. If is a partition of n + 1 , w e denote by =ij the diagram obtained by removing the cell i; j from the French Ferrers diagram of. We set =ij = det k x pj i y qj be the linear span of the partial derivatives of =ij. The bihomogeneity o f =ij and its alternating nature under the diagona...
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We construct a family of functors assigning an R-module to a flag of R-modules, where R is a commutative ring. As particular instances, we get flagged Schur functors and Schubert functors, the latter family being indexed by permutations. We identify Schubert functors for vexillary permutations with some flagged Schur functors, thus establishing a functorial analogue of a theorem from [6] and [1...
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The task of a theory of Schubert polynomials is to produce explicit representatives for Schubert classes in the cohomology ring of a flag variety, and to do so in a manner that is as natural as possible from a combinatorial point of view. To explain more fully, let us review a special case, the Schubert calculus for Grassmannians, where one asks for the number of linear spaces of given dimensio...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1999
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2931