论文标题
Jacobi Triple Product和Rogers-Ramanujan身份的平铺证明
Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities
论文作者
论文摘要
我们使用平铺方法为一些著名的$ Q $ series身份提供基本组合证明，例如Jacobi Triple Triple Product Identity，Rogers-Ramanujan身份以及一些Rogers的身份。我们给出了Q-Binomial定理的平铺证明和Q-二项式系数的平铺解释。还可以通过使用“瓷砖方法”获得新的广义$ k $ - 产品$ q $ series身份，其中矩形板的所有可能瓷砖的生成功能以两种不同的方式计算以获得所需的$ q $ $ series Identity。还建立了几个新的递归$ q $ series身份。 “平铺方法”有望提供美学上令人愉悦的方法来证明新旧$ q $ series的身份。
We use the method of tiling to give elementary combinatorial proofs of some celebrated $q$-series identities, such as Jacobi triple product identity, Rogers-Ramanujan identities, and some identities of Rogers. We give a tiling proof of the q-binomial theorem and a tiling interpretation of the q-binomial coefficients. A new generalized $ k $-product $q$-series identity is also obtained by employing the `tiling-method', wherein the generating function of the set of all possible tilings of a rectangular board is computed in two different ways to obtain the desired $q$-series identity. Several new recursive $ q$-series identities were also established. The `tiling-method' holds promise for giving an aesthetically pleasing approach to prove old and new $q$-series identities.
