Agrachev, A. A.; Gamkrelidze, R. V. 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]. Cited in 5 Documents MSC: 05E15 Combinatorial aspects of groups and algebras (MSC2010) 20B30 Symmetric groups 17B35 Universal enveloping (super)algebras 05A05 Permutations, words, matrices Keywords:symmetric groups; Volterra series; shuffle product; permutations PDFBibTeX XMLCite \textit{A. A. Agrachev} and \textit{R. V. Gamkrelidze}, Lect. Notes Pure Appl. Math. 152, 365--382 (1994; Zbl 0790.05095)