论文标题
简单的六角形晶格和11杆结的分类
Bounds in simple hexagonal lattice and classification of 11-stick knots
论文作者
论文摘要
在简单的六角晶格（SH-lattice）中，打结类型的棍棒数和边缘长度分别是所需的棍棒和边缘数量最小，以构建SH-lattice的给定类型的结。通过引入晶格之间的线性变换，我们证明，对于任何给定的结，SH晶格中的两个值都严格少于立方晶格中的值。最后，我们表明，SH-lattice中唯一的非平凡的11棒结是Trefoil结（$ 3_1 $）和Figure-oight结（$ 4_1 $）。
The stick number and the edge length of a knot type in the simple hexagonal lattice (sh-lattice) are the minimal numbers of sticks and edges required, respectively, to construct a knot of the given type in sh-lattice. By introducing a linear transformation between lattices, we prove that for any given knot both values in the sh-lattice are strictly less than the values in the cubic lattice. Finally, we show that the only non-trivial 11-stick knots in the sh-lattice are the trefoil knot ($3_1$) and the figure-eight knot ($4_1$).
