Equidistribution and partition polynomials
Equidistribution and partition polynomials
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DOI：
10.1007/s11139-023-00762-w
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
A. Folsom;Joshua Males;Larry Rolen
中科院分区：
文献类型：
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作者：
A. Folsom;Joshua Males;Larry Rolen
利用等分布准则，我们建立了几个分区多项式的分圆多项式的整除性，包括spt-曲柄，overpartition对，和t-核心分区。作为推论，我们得到了新的证明各种Ramanujan型同余相关联的分区功能。此外，利用Erdös和Turán的结果，我们建立了单位圆上分割多项式的根的等分布，包括秩，曲柄，spt和单峰序列。我们的研究结果补充了Stanley，Boyer-Goh和其他人关于这个主题的早期工作。我们解释了如何使用我们的方法来建立类似的结果，其他分区多项式的利益，并提供了许多相关的公开问题和例子。
Using equidistribution criteria, we establish divisibility by cyclotomic polynomials of several partition polynomials of interest, includingspt-crank, overpartition pairs, andt-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.