Small knot mosaics and partition matrices
Small knot mosaics and partition matrices
复制标题
小结马赛克和分区矩阵
DOI：
10.1088/1751-8113/47/43/435201
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Seungsang Oh
中科院分区：
文献类型：
--
作者：
Kyungpyo Hong;Ho Lee;Hwa Jeong Lee;Seungsang Oh
洛摩纳哥和考夫曼引入了纽结马赛克系统，给出了量子纽结系统的定义。这个定义旨在代表一个实际的物理量子系统。纽结(m，n)-马赛克是所描绘的从T0到T10的马赛克瓦片的m×n矩阵，表示通过适当邻接而被称为适当连接的纽结或链接。研究马赛克理论的一个有趣的问题是，(m，n)-马赛克有多少个。Dm，n>；表示所有纽结(m，n)-马赛克的总数。这个计数是非常重要的，因为节马赛克的总数实际上就是这些量子节马赛克的希尔伯特空间的维度。本文给出了4≦̸m≦̸n≦̸6？>；的Dm，n？我们主要使用划分矩阵参数，这被证明在计算小结马赛克时非常有效。
Lomonaco and Kauffman introduced knot mosaic system to give a definition of quantum knot system. This definition is intended to represent an actual physical quantum system. A knot (m, n)-mosaic is an m × n ?> matrix of mosaic tiles which are T0 through T10 depicted, representing a knot or a link by adjoining properly that is called suitably connected. An interesting question in studying mosaic theory is how many knot (m, n)-mosaics are there. D m , n ?> denotes the total number of all knot (m, n)-mosaics. This counting is very important because the total number of knot mosaics is indeed the dimension of the Hilbert space of these quantum knot mosaics. In this paper, we find a table of the precise values of D m , n ?> for 4 ≦̸ m ≦̸ n ≦̸ 6 ?> . Mainly we use a partition matrix argument which turns out to be remarkably efficient to count small knot mosaics.