论文标题
最大$ p $ -core $ p'$ - 分区的渐近属性
Asymptotic Properties of Maximal $p$-Core $p'$-Partitions
论文作者
论文摘要
对于Primes $ p $，我们研究了$ p $ $ p'$ - 分区的最大大小（无钩长度或零件可除以$ p $的分区）。麦克道威尔最近证明，最大值是由唯一的分区（例如$λ_p$）实现的。使用他的图形理论描述$λ_p$，我们证明$ p> 10^6 $ tht \ [\ frac {1} {24} {24} p^6 -p^5 \ sqrt {p} <|λ_p| <\ frac {1} {24} p^6- \ frac {1} {200} p^5 \ sqrt {p}，\]，这表明$ |λ_p| \ sim p^6/24 $ as $ p \ to \ infty $。
For primes $p$, we study the maximal possible size of a $p$-core $p'$-partition (a partition with no hook lengths or parts divisible by $p$). McDowell recently proved that the maximum is attained by a unique partition, say $Λ_p$. Using his graph theoretic description of $Λ_p$, we prove for $p > 10^6$ that \[\frac{1}{24}p^6 - p^5\sqrt{p} < |Λ_p| < \frac{1}{24}p^6 - \frac{1}{200}p^5\sqrt{p},\] which shows that $|Λ_p| \sim p^6/24$ as $p \to \infty$.
