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On n-associative formal power series |
Aequationes mathematicae 90, 449-467, (2016). DOI 10.1007/s00010-015-0372-0
Abstract. A formal power series F(x1,…,xn)∈ ℂ [[x1,…,xn]] of order at least 1 is called n-associative, n≥ 3, if
This notion generalizes associativity which is the special case of n=2. We determine the set of all n-associative formal power series over ℂ, all convergent n-associative power series, and all commutative (or symmetric) n-associative formal power series. Moreover we study relations between n- and m-associativity for certain n,m∈ ℕ and determine the structure of associative families (Fn)n≥ 1 of formal power series Fn(x1,…,xn)∈ ℂ [[x1,…,xn]].
F(F(x1,…,xn),xn+1,…,x2n-1)=…= F(x1,…,xn-1,F(xn,xn+1,…,x2n-1))...
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GDPR | On n-associative formal power series |  |