Some Combinatorial Properties of Schubert Polynomials
Some Combinatorial Properties of Schubert Polynomials
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DOI：
10.1023/a:1022419800503
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发表时间：
1993-11
影响因子：
0.8
通讯作者：
Sara C. Billey;William Jockusch;R. Stanley
中科院分区：
文献类型：
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作者：
Sara C. Billey;William Jockusch;R. Stanley
舒伯特多项式由Bernstein et al.和Demazure引入，并由Lascoux、sch<s:1>岑伯格、Macdonald等人广泛发展。我们给出了舒伯特多项式的显式组合解释，即排列的简化分解。利用这一结果，由Edelman和Greene提出的Schensted对应关系的一种变体允许人们以一种自然的方式将某一组场景与w联系起来，每个场景贡献一个术语。这种对应关系导致了许多问题和猜想，并对其相互关系进行了研究。在第2节中，我们考虑长度为3的无递减子序列的排列（或321避免排列）。我们证明了对于这样的排列，它是一个旗偏舒尔函数。在第3节中，我们使用这个结果来获得有理函数的一些有趣的性质，其中表示一个倾斜舒尔函数。
Schubert polynomials were introduced by Bernstein et al. and Demazure, and were extensively developed by Lascoux, Schützenberger, Macdonald, and others. We give an explicit combinatorial interpretation of the Schubert polynomialin terms of the reduced decompositions of the permutationw. Using this result, a variation of Schensted's correspondence due to Edelman and Greene allows one to associate in a natural way a certain setof tableaux withw, each tableau contributing a single term to. This correspondence leads to many problems and conjectures, whose interrelation is investigated. In Section 2 we consider permutations with no decreasing subsequence of length three (or 321-avoiding permutations). We show for such permutations thatis aflag skew Schur function. In Section 3 we use this result to obtain some interesting properties of the rational function, wheredenotes a skew Schur function.