RC-Graphs and Schubert Polynomials
RC-Graphs and Schubert Polynomials
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RC 图和舒伯特多项式
DOI：
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发表时间：
1993
影响因子：
0.5
通讯作者：
Sara C. Billey
中科院分区：
文献类型：
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作者：
N. Bergeron;Sara C. Billey
贝杰隆得到了国家科学基金会的支持。比利得到了国家物理科学联盟、IBM和UCSD的支持。使用公式的比利，Jockusch和斯坦利，福明和基里洛夫介绍了一组新的图表编码的舒伯特多项式。我们称这些对象为rc-图。我们定义并证明了两个变种的算法，用于构建一个给定的置换的所有rc-图的集合。这种构造使得许多已知的舒伯特多项式的恒等式更加明显，并产生新的恒等式。特别是，我们给出了一个新的证明蒙克的规则使用插入算法的rc-图。我们猜想两个类似的Pieri的规则乘以舒伯特多项式。我们还将该算法推广到生成双Schubert多项式。
Bergeron was supported by the National Science Foundation. Billey was supported by the National Physical Science Consortium, IBM and UCSD. Using a formula of Billey, Jockusch and Stanley, Fomin and Kirillov have introduced a new set of diagrams that encode the Schubert polynomials. We call these objects rc-graphs. We define and prove two variants of an algorithm for constructing the set of all rc-graphs for a given permutation. This construction makes many of the identities known for Schubert polynomials more apparent, and yields new ones. In particular, we give a new proof of Monk’s rule using an insertion algorithm on rc-graphs. We conjecture two analogs of Pieri’s rule for multiplying Schubert polynomials. We also extend the algorithm to generate the double Schubert polynomials.