Characterization of non-self OU sequences of two-component link diagrams
Naoki Sakata, Ayaka Shimizu, Koya Shimokawa
TL;DR
This paper investigates the information contained in non-self OU sequences of two-component link diagrams, providing a complete characterization of such sequences for these links and specific prime links with up to five crossings.
Contribution
It offers a complete characterization of pairs of non-self OU sequences for two-component links and certain prime links, advancing understanding of link diagram invariants.
Findings
Characterized pairs of non-self OU sequences for two-component links
Extended characterization to prime links with up to five crossings
Enhanced understanding of link diagram crossing information
Abstract
A non-self OU sequence is a cyclic sequence of crossing information of non-self crossings that is obtained by traversing a knot component of an oriented link diagram. In this paper, we investigate what information can be derived from non-self OU sequences, and we completely characterize pairs of non-self OU sequences of diagrams of two-component links. We also characterize the pairs for specific prime links with crossing number up to five.
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