Explicit Polynomial Generators for the Ring of Quasisymmetric Functions over the Integers
Explicit Polynomial Generators for the Ring of Quasisymmetric Functions over the Integers
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DOI：
10.1007/s10440-009-9439-z
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发表时间：
2004-10
影响因子：
1.6
通讯作者：
M. Hazewinkel
中科院分区：
文献类型：
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作者：
M. Hazewinkel
在（Hazewinkel in Adv. Math. 164：283-300，2001，and CWI preprint，2001）中已经证明了整数上的拟对称函数环是自由多项式。这是一个问题，一直是极大的兴趣，自1972年以来，例如，因为这一声明中的作用，在分类理论的非交换正式团体，一直在发展，自那时以来，见（迪特在发明。17：1-20，1972; in Scholtens' Thesis，Free Univ. of Amsterdam，1996）和后者中的参考文献。同时，准对称函数已经发现了更多的应用（参见Gel ′ fand等人，Adv.Math.112：218-348，1995）。然而，作者在上述论文中的证明并没有给出QSymmover整数的显式多项式生成器。在这篇文章中，我给出了一组（非常简单的）多项式生成器，用于QSymmover整数。
In (Hazewinkel in Adv. Math. 164:283–300, 2001, and CWI preprint, 2001) it has been proved that the ring of quasisymmetric functions over the integers is free polynomial. This is a matter that has been of great interest since 1972; for instance because of the role this statement plays in a classification theory for noncommutative formal groups that has been in development since then, see (Ditters in Invent. Math. 17:1–20, 1972; in Scholtens’ Thesis, Free Univ. of Amsterdam, 1996) and the references in the latter. Meanwhile quasisymmetric functions have found many more applications (see Gel’fand et al. in Adv. Math. 112:218–348, 1995). However, the proofs of the author in the aforementioned papers do not give explicit polynomial generators forQSymmover the integers. In this note I give a (really quite simple) set of polynomial generators forQSymmover the integers.