论文标题
等分和分区多项式
Equidistribution and partition polynomials
论文作者
论文摘要
使用等分分配标准，我们通过几个分区的多项式多项式（包括$ spt $ crank，crank，过度分支机构和$ t $ core-core分区）建立了分区。作为推论，我们获得了各种Ramanujan型的新证明，以赋予相关的分区功能。此外，使用Erdös和Turán的结果，我们在单位圆圈上建立了分区多项式根的等分分配，包括等级，曲柄，$ spt $和单峰序列的序列。我们的结果补充了Stanley，Boyer-Goh等关于此主题的早期工作。我们解释了如何使用我们的方法为其他感兴趣的多项式分区建立相似的结果，并提供许多相关的开放问题和示例。
Using equidistribution criteria, we establish divisibility by cyclotomic polynomials of several partition polynomials of interest, including $spt$-crank, overpartition pairs, and $t$-core partitions. As corollaries, we obtain new proofs of various Ramanujan-type congruences for associated partition functions. Moreover, using results of Erdös and Turán, we establish the equidistribution of roots of partition polynomials on the unit circle including those for the rank, crank, $spt$, and unimodal sequences. Our results complement earlier work on this topic by Stanley, Boyer-Goh, and others. We explain how our methods may be used to establish similar results for other partition polynomials of interest, and offer many related open questions and examples.
