Balanced Labellings and Schubert Polynomials
نویسندگان
چکیده
منابع مشابه
Balanced Labellings and Schubert Polynomials
We study balanced labellings of diagrams representing the inversions in a permutation. These are known to be natural encodings of reduced decompositions of permutations w 2 n , and we show that they also give combinatorial descriptions of both the Stanley symmetric functions F w and and the Schubert polynomial S w associated with w. Furthermore, they lead to an explicit basis for the Schubert m...
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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 aim of this paper is to introduce some polynomials that specialize to all previously known Schubert polynomials: the classical Schubert polynomials of Lascoux and Schützenberger [L-S], [M], the quantum Schubert polynomials of Fomin, Gelfand, and Postnikov [F-G-P], and quantum Schubert polynomials for partial flag varieties of Ciocan-Fontanine [CF2]. There are also double versions of these u...
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where In is the ideal generated by symmetric polynomials in x1, . . . , xn without constant term. Another, geometric, description of the cohomology ring of the flag manifold is based on the decomposition of Fln into Schubert cells. These are even-dimensional cells indexed by the elements w of the symmetric group Sn . The corresponding cohomology classes σw , called Schubert classes, form an add...
متن کاملSkew Schubert Polynomials
We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in Bruhat order of the symmetric group. These skew Schubert polynomials expand in the basis of Schub...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1997
ISSN: 0195-6698
DOI: 10.1006/eujc.1996.0109