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Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

✍ Scribed by Gérard H. E. Duchamp; Florent Hivert; Jean-Christophe Novelli; Jean-Yves Thibon


Book ID
105764900
Publisher
Springer
Year
2011
Tongue
English
Weight
349 KB
Volume
15
Category
Article
ISSN
0218-0006

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Let Fc denote the basic quasi-symmetric functions, in Gessel's notation (1984) (C any composition). The plethysm sz oFc is a positive linear combination of functions Fo. Under certain conditions, the image under the involution ~o of a quasi-symmetric function defined by equalities and inequalities o

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Let Z denote the Leibniz-Hopf algebra, which also turns up as the Solomon descent algebra and the algebra of noncommutative symmetric functions. As an algebra Z=ZOZ 1 , Z 2 , ...P, the free associative algebra over the integers in countably many indeterminates. The coalgebra structure is given by m(