What type of study is this?

This is a Quantitative Study study.

October 16, 2025

Infinitely many virtual knots with any given sequence of n-writhes

Key Points

Infinitely many virtual knots exist with varied properties based on specified sequences.
The study introduces a novel approach using vertex connected sums on Gauss diagrams.
Notably, each virtual knot exhibits an unknotting number of one.
The concept of n-writhe serves as a key invariant for understanding these knots.

Abstract

Satoh and Taniguchi introduced the Formula: see text-writhe Formula: see text for each non-zero integer Formula: see text, which is an integer invariant for virtual knots. It is obvious that the virtualization of a real crossing is an unknotting operation for virtual knots. In our previous paper, we showed that if Formula: see text is a sequence of integers with Formula: see text, then there exists a virtual knot Formula: see text whose virtual unknotting number equals one and Formula: see text for any Formula: see text. In this paper we show that there exist infinitely many virtual knots having such properties by using the vertex connected sum on Gauss diagrams.

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Cite This Study

OHYAMA et al. (Wed,) studied this question.

synapsesocial.com/papers/68f04acce559138a1a06ea27 https://doi.org/https://doi.org/10.1142/s0218216525500920

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