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On partitions and cyclotomic polynomials. (English) Zbl 1067.11510
Summary: Let \(m\) denote a squarefree number. Let \(f_m(n)\) denote the number of partitions of \(n\) into parts that are relatively prime to \(m\). Let \(\Phi_m(z)\) denote the \(m\)th cyclotomic polynomial. We obtain a generating function for \(f_m(n)\) that involves factors \(\Phi_m(z^n)\).
MSC:
11P81 Elementary theory of partitions
05A17 Combinatorial aspects of partitions of integers
11T22 Cyclotomy
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