منابع مشابه
Qsym over Sym is free
Astract We study here the ring QSn of Quasi-Symmetric Functions in the variables x1, x2, . . . , xn. F. Bergeron and C. Reutenauer [4] formulated a number of conjectures about this ring, in particular they conjectured that it is free over the ring Λn of symmetric functions in x1, x2, . . . , xn. We present here an algorithm that recursively constructs a Λn-module basis for QSn thereby proving o...
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We prove that the subset of quasisymmetric polynomials conjectured by Bergeron and Reutenauer to be a basis for the coinvariant space of quasisymmetric polynomials is indeed a basis. This provides the first constructive proof of the Garsia–Wallach result stating that quasisymmetric polynomials form a free module over symmetric polynomials and that the dimension of this module is n!.
متن کاملStably free modules over R[X] of rank > dim R are free
We prove that for any finite-dimensional ringR and n ≥ dimR+2, the group En(R[X]) acts transitively on Umn(R[X]). In particular, we obtain that for any finite-dimensional ringR, all finitely generated stably free modules over R[X] of rank > dimR are free. This result was only known for Noetherian rings. The proof we give is short, simple, and constructive.
متن کامل-torsion free Acts Over Monoids
In this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. Then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right Rees factor, cyclic and acts in general implies some other properties, respectively.
متن کاملQuasi-symmetric functions, multiple zeta values, and rooted trees
The algebra Sym of symmetric functions is a proper subalgebra of QSym: for example, M11 and M12 +M21 are symmetric, but M12 is not. As an algebra, QSym is generated by those monomial symmetric functions corresponding to Lyndon words in the positive integers [11, 6]. The subalgebra of QSym ⊂ QSym generated by all Lyndon words other than M1 has the vector space basis consisting of all monomial sy...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2007
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2006.08.009