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%           FPSAC/SFCA '94, May 23-27, 1994   at DIMACS
%                     Problem Session
%   LaTeX file of problem submitted by Francois Bergeron (May 24, 1994)
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\begin{center}
{FPSAC/SFCA '94}\\
{PROBLEM SESSION}\\
{Submission received May 24, 1994}\\[.2in]
{\bf POSITIVE POWER SERIES}\\[.1in]
Fran\c{c}ois Bergeron\\[.2in]
\end{center}
Characterize series $c(t) = \sum c_nt^n$, with $c_0=1$, such that for
all partitions $\lambda\vdash m\geq 1$, the power series
  $$ \frac{1}{c(t)}s_{\lambda}[c(t)] $$
\noindent has nonnegative integer coefficients. Here $s_{\lambda}$ is
a Schur function and $[c(t)]$ denotes $\lambda$-ring substitution,
i.e., $p_k[c(t)] = c(t^k)$ and $f[c(t)]$ is additive and
multiplicative, where $p_k$ is a power sum symmetric function. A
nontrivial series which satisfies the condition is $c(t) =
1/\sqrt{1-4t}$.
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