Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial
Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial
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Rogers-Ramanujan 型恒等式以及彩色琼斯多项式的头尾
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发表时间：
2011
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通讯作者：
Oliver T. Dasbach
中科院分区：
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作者：
Cody Armond;Oliver T. Dasbach
我们研究有色Jones多项式的头部和尾部，同时主要集中在交替链接上。计算给定链节的有色琼斯多项式的各种方法都会得到这些幂函数级数的组合恒等式。我们进一步证明了头函数和尾函数仅依赖于纽结图的简化棋盘图。此外，素数交错链环的头部和尾部函数类构成么半群。
We study the head and tail of the colored Jones polynomial while focusing mainly on alternating links. Various ways to compute the colored Jones polynomial for a given link give rise to combinatorial identities for those power series. We further show that the head and tail functions only depend on the reduced checkerboard graphs of the knot diagram. Moreover the class of head and tail functions of prime alternating links forms a monoid.