Elementary Polynomial Identities Involving $$\varvec{q}$$-Trinomial Coefficients
Elementary Polynomial Identities Involving $$\varvec{q}$$-Trinomial Coefficients
复制标题
涉及 $$varvec{q}$$-三项式系数的初等多项式恒等式
DOI：
10.1007/s00026-019-00445-8
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发表时间：
2019
影响因子：
0.5
通讯作者：
A. Uncu
中科院分区：
文献类型：
--
作者：
A. Berkovich;A. Uncu
利用q-二项式定理证明了三个新的q-三项式系数多项式恒等式。然后，我们使用求和公式的q-三项式系数转换成另一组的三个多项式的身份，这意味着卡帕雷利的分区定理时，多项式的程度趋于无穷大。这样，我们也得到了一个有趣的新结果的总和的Capparelli的产品。最后，我们提出了一个无限层次的多项式身份。
We use the q-binomial theorem to prove three new polynomial identities involving q-trinomial coefficients. We then use summation formulas for the q-trinomial coefficients to convert our identities into another set of three polynomial identities, which imply Capparelli’s partition theorems when the degree of the polynomial tends to infinity. This way we also obtain an interesting new result for the sum of the Capparelli’s products. We finish this paper by proposing an infinite hierarchy of polynomial identities.