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Partitions and Truncations
Let $P(x)=\sum_{n=0}^{\infty} p_nx^n$ be the partition generating function, and let $P^*(x)=\sum_{n=0}^{\infty} p^*_nx^n$, where
$$p^*_n = \binom{\text{number of partitions of }n}{\text{into an even ...
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Compositions and Partitions
For a nonnegative integer $n$, a composition of $n$ means a partition in which the order of the parts matters. For example, the compositions of $3$ are $3$, $2+1$, $1+2$, and $1+1+1$.
Consider the ...
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Truncation of partitions generating function question
$A (x)$ is the generating function for partitions. $B(x)=\sum_{n=0}^{\infty}b_nx^n $
$$b_n =\binom{\text{number of partitions of }n}{\text{into an even number of parts}}-\binom{\text{number of ...
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