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The shuffle product and symmetric groups. (English) Zbl 0790.05095

Elworthy, K.D. (ed.) et al., Differential equations, dynamical systems, and control science. A Festschrift in Honor of Lawrence Markus. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 152, 365-382 (1994).
Summary: The shuffle product of permutations is investigated. This operation is an algebraic model of the standard triangulation of the Cartesian product of simplexes. A nontrivial connection is established between the shuffle product and the usual composition product of permutations, which leads to interesting algebraic-combinatorial implementations.
For the entire collection see [Zbl 0780.00045].

MSC:

05E15 Combinatorial aspects of groups and algebras (MSC2010)
20B30 Symmetric groups
17B35 Universal enveloping (super)algebras
05A05 Permutations, words, matrices
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