Counting alternating knots by genus
Counting alternating knots by genus
复制标题
按属计数交替结
DOI：
10.1007/s00208-005-0659-x
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发表时间：
2005
影响因子：
1.4
通讯作者：
A. Vdovina
中科院分区：
文献类型：
--
作者：
A. Stoimenow;A. Vdovina
结果表明，给定属 g>1 的交替结的数量在交叉数中以 6g−4 次多项式的形式增长。多项式的首项系数取决于交叉数的奇偶性，与具有比勒路径的平面三价图相关。估计此类图的数量的增长率。
It is shown that the number of alternating knots of given genus g>1 grows as a polynomial of degree 6g−4 in the crossing number. The leading coefficient of the polynomial, which depends on the parity of the crossing number, is related to planar trivalent graphs with a Bieulerian path. The rate of growth of the number of such graphs is estimated.