Quasi-Symmetric Functions

Michiel Hazewinkel ()
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Michiel Hazewinkel: CWI

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 30-44 from Springer

Abstract: Abstract 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 = Z , the free associative algebra over the integers in countably many indeterminates. The co-algebra structure is given by $$\mu({Z_n})=\sum\nolimits_{i = 0}^n{{Z_i}}\otimes{Z_{n-i}}$$ , Z 0 = 1. Let M be the graded dual of Z. This is the algebra of quasi-symmetric functions. The Ditters conjecture (1972), says that this algebra is a free commutative algebra over the integers. This was proved in [13]. In this paper I give an outline of the proof and discuss a number of consequences and related matters.

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_3

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