The F-polynomial invariant for knotoids

As a generalization of the classical knots, knotoids deal with the open ended knot diagram in a surface. In recent years, many polynomial invariants for knotoids appeared, such as the bracket polynomial, the index polynomial and the [Formula: see text]th polynomial. In this paper, we introduce a new polynomial invariant [Formula: see text]-polynomial for knotoids and discuss some properties of the [Formula: see text]-polynomial. Finally, we construct a family of knotoid diagrams which can be distinguished from each other by the [Formula: see text]-polynomial but cannot be distinguished by the index polynomial and the [Formula: see text]th polynomial.