Polynomial identities implying Capparelli's partition theorems
Polynomial identities implying Capparelli's partition theorems
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隐含卡帕雷利分区定理的多项式恒等式
DOI：
10.1016/j.jnt.2019.02.028
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发表时间：
2018
影响因子：
0.7
通讯作者：
A. Uncu
中科院分区：
文献类型：
--
作者：
A. Berkovich;A. Uncu
我们提出并递归地证明了包含Capparelli分拆定理的多项式恒等式。我们也找到了与Andrews，以及Alladi，Andrews和Gordon关于q-三项式系数的结果的完美伴侣。我们遵循Kurşungöz的想法，为我们的一些表达提供直接的组合解释。我们利用Bailey引理的三项式类比来导出新的恒等式。这些恒等式与某些三重和乘积有关。还证明了涉及基Q2、Q3、Q6和Q12的几个新的Slett型恒等式。我们还讨论了一个新的无穷族，它包含了这些斯莱特型恒等式。
We propose and recursively prove polynomial identities which imply Capparelli's partition theorems. We also find perfect companions to the results of Andrews, and Alladi, Andrews and Gordon involving q-trinomial coefficients. We follow Kurşungöz's ideas to provide direct combinatorial interpretations of some of our expressions. We make use of the trinomial analogue of Bailey's lemma to derive new identities. These identities relate certain triple sums and products. A couple of new Slater type identities involving bases q 2, q 3, q 6, and q 12 are also proven. We also discuss a new infinite hierarchy containing these Slater type identities.