The $F$-polynomial invariant for knotoids

Yi Feng; Fengling Li

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arXiv · 2312.16058

The $F$-polynomial invariant for knotoids

Yi Feng·Fengling Li

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Abstract

As a generalization of the classical knots, knotoids deal with the open ended knot diagrams in a surface. In recent years, many polynomial invariants for knotoids have appeared, such as the bracket polynomial, the index polynomial and the $n$th polynomial, etc. In this paper, we introduce a new polynomial invariant $F$-polynomial for knotoids and discuss some properties of the $F$-polynomial. Then, we construct a family of knotoid diagrams which can be distinguished from each other by the $F$-polynomial but cannnot be distinguished by the index polynomial and the $n$th polynomial.

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BibTeX RIS

Yi Feng, Fengling Li. 2023-12-26. The $F$-polynomial invariant for knotoids. https://arxiv.org/abs/2312.16058

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