{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/boltzmann-enhancements-of-biquasile-counting","title":"Boltzmann Enhancements of Biquasile Counting Invariants","arxiv_id":"1704.02555","date":"2017-04-09","proceeding":null,"authors":["WonHyuk Choi","Deanna Needell","Sam Nelson"],"abstract":"In this paper, we build on the biquasiles and dual graph diagrams introduced in arXiv:1610.06969. We introduce \\textit{biquasile Boltzmann weights} that enhance the previous knot coloring invariant defined in terms of finite biquasiles and provide examples differentiating links with the same counting invariant, demonstrating that the enhancement is proper. We identify conditions for a linear function $\\phi:\\mathbb{Z}_n[X^3]\\to\\mathbb{Z}_n$ to be a Boltzmann weight for an Alexander biquasile $X$.","url_abs":"https://arxiv.org/abs/1704.02555v3","url_pdf":"https://arxiv.org/pdf/1704.02555v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"boltzmann-enhancements-of-biquasile-counting","repo_url":"https://github.com/wonhyukchoi/biquasiles","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}