Alternating knots, planar graphs, and $$q$$q-series
Alternating knots, planar graphs, and $$q$$q-series
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交替结、平面图和 $$q$$q 系列
DOI：
10.1007/s11139-014-9592-5
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Thao Vuong
中科院分区：
文献类型：
--
作者：
S. Garoufalidis;Thao Vuong
量子拓扑学的最新进展至少以三种不同的方式将-序列分配给节点。该级数由广义Nahm和给出（即，特殊超几何和），并有未知的模块和渐近性质。我们给出了一个有效的方法来计算这些系列来自平面图（即，减少Tait图的交替链接）和计算的几个条款，这些系列的所有图，最多有8个边得出几个结论。此外，我们给出了一个定理的Dasbach-Lin的图论证明，该定理确定了在这些系列中的系数为多项式的顶点，边和三角形的图形的数量。
Recent advances in Quantum Topology assign-series to knots in at least three different ways. The-series are given by generalized Nahm sums (i.e., special-hypergeometric sums) and have unknown modular and asymptotic properties. We give an efficient method to compute those-series that come from planar graphs (i.e., reduced Tait graphs of alternating links) and compute several terms of those series for all graphs with at most 8 edges drawing several conclusions. In addition, we give a graph-theory proof of a theorem of Dasbach-Lin which identifies the coefficient ofin those series forin terms of polynomials on the number of vertices, edges, and triangles of the graph.