Crosscap numbers of alternating links via state codes

Isaias Bahena; Thomas Kindred; Jason Parsley

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arXiv · 2512.09887

Crosscap numbers of alternating links via state codes

Isaias Bahena·Thomas Kindred·Jason Parsley

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Abstract

We describe a way of encoding a Kauffman state as a set of tuples, similar to a Gauss code. Then we describe a procedure for using these state codes to determine the unoriented genus and crosscap number of any prime alternating knot or link. Finally, we compute these values for all such links through 14 crossings and all such knots through 19 crossings (this data is new for links with 10-14 crossings and knots with 14-19 crossings), and we identify several intriguing patterns in the resulting data.

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Isaias Bahena, Thomas Kindred, Jason Parsley. 2025-12-10. Crosscap numbers of alternating links via state codes. https://arxiv.org/abs/2512.09887

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