Abstract 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 S U ( 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.

中文翻译：

---

区分突变结

摘要 结理论受到物理学家和数学家的积极研究，因为它为许多物理和数学理论提供了连接核心。结理论中具有挑战性的问题之一是区分突变结。对于由 SU ( N ) 的对称和或反对称表示着色的结，突变结不通过有色 HOMFLY-PT 多项式区分。一些突变结可以通过最简单的非对称表示来区分 [2, 1]。然而，有一类突变结需要更复杂的表示，如 [4, 2]。在本文中，我们计算了表示 [3, 1] 和 [4, 2] 中突变结多项式的多项式和差异，并研究了它们的性质。