论文标题
区分突变结
Distinguishing Mutant Knots
论文作者
论文摘要
结理论是由物理学家和数学家积极研究的，因为它为许多物理和数学理论提供了连接的核心。结理论中具有挑战性的问题之一是区分突变结。突变结不会通过$ su（n）$的对称和 /或反对称表示的彩色打结来区分。一些突变结可以通过最简单的非对称表示$ [2,1] $来区分。但是，有一类突变结需要更复杂的表示，例如$ [4,2] $。在本文中，我们计算了表示$ [3,1] $和$ [4,2] $中的多项式多项式的多项式和差异，并研究其属性。
Knot theory is actively studied both by physicists and mathematicians as it provides a connecting centerpiece for many physical and mathematical theories. One of the challenging problems in knot theory is distinguishing mutant knots. Mutant knots are not distinguished by colored HOMFLY-PT polynomials for knots colored by either symmetric and or antisymmetric representations of $SU(N)$. Some of the mutant knots can be distinguished by the simplest non-symmetric representation $[2,1]$. However there is a class of mutant knots which require more complex representations like $[4,2]$. In this paper we calculate polynomials and differences for the mutant knot polynomials in representations $[3,1]$ and $[4,2]$ and study their properties.
