23 research outputs found

    Exposure to violence in breast cancer patients: systematic review

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    PMID = 3013607

    Monogenic pure cubics

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    <i>N</i>-colored generalized Frobenius partitions: generalized Kolitsch identities

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    AbstractLet N1N\geq 1 be squarefree with (N,6)=1(N,6)=1 . Let cϕN(n)c\phi _N(n) denote the number of N-colored generalized Frobenius partitions of n introduced by Andrews in 1984, and P(n)P(n) denote the number of partitions of n. We prove cϕN(n)=dNN/dP(Nd2nN2d224d2)+b(n), \begin{align*}c\phi_N(n)= \sum_{d \mid N} N/d \cdot P\left( \frac{ N}{d^2}n - \frac{N^2-d^2}{24d^2} \right) + b(n),\end{align*} where C(z):=(q;q)Nn=1b(n)qnC(z) := (q;q)^N_\infty \sum _{n=1}^{\infty } b(n) q^n is a cusp form in S(N1)/2(Γ0(N),χN)S_{(N-1)/2} (\Gamma _0(N),\chi _N) . This extends and strengthens earlier results of Kolitsch and Chan–Wang–Yan treating the case when N is a prime. As an immediate application, we obtain an asymptotic formula for cϕN(n)c\phi _N(n) in terms of the classical partition function P(n)P(n) .</jats:p
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