We show that there are biases in the number of appearances of the parts in two residue classes in the set of ordinary partitions. More precisely, let $p_{j,k,m} (n)$ be the number of partitions of n such that there are more parts congruent to j modulo m than parts congruent to k modulo m for $m \geq 2$ . We prove that $p_{1,0,m} (n)$ is in general larger than $p_{0,1,m} (n)$ . We also obtain asymptotic formulas for $p_{1,0,m}(n)$ and $p_{0,1,m}(n)$ for $m \geq 2$ .

中文翻译：

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整数分区中的偏差

我们表明，在普通分区集合中，两个残差类别中的零件出现次数存在偏差。更准确地说，让$p_{j,k,m} (n)$是的分区数n这样有更多的部分一致j模数米比部分一致ķ模数米为了$m \geq 2$. 我们证明$p_{1,0,m} (n)$一般大于$p_{0,1,m} (n)$. 我们还获得了渐近公式$p_{1,0,m}(n)$和$p_{0,1,m}(n)$为了$m \geq 2$.