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Noncommutative symmetric functions. VI: Free quasi-symmetric functions and related algebras. (English) Zbl 1027.05107
The authors study several algebras related to symmetric functions the natural bases of which can be labelled by various combinatorial objects: permutations, standard Young tableaux and packed integer matrices. Also, they discuss new examples of indecomposable \(H_n(0)\)-modules and compute their homological properties for small \(n\). At the end, the algebra of matrix quasi-symmetric functions is interpreted as a convolution algebra.

MSC:
05E05 Symmetric functions and generalizations
20C08 Hecke algebras and their representations
06A11 Algebraic aspects of posets
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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