{"ID":23595654,"CreatedAt":"2026-09-18T05:42:42.291333095Z","UpdatedAt":"2026-09-18T05:42:42.291333095Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20413","arxiv_id":"2609.20413","title":"Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial","abstract":"The linking number and coefficients of the Conway polynomial are two examples of finite type invariants. Goussarov-Polyak-Viro proved that any finite type knot invariant can be computed in a two step process, where the second step is referred to as the GPV map for the invariant. This paper computes the GPV maps for the linking number and low-degree coefficients of the Conway Polynomial. Chmutov-Khoury-Rossi gave one description of the GPV maps for coefficients of the Conway polynomial in terms of arrow diagrams and state-sum calculations. We take a much more grounded approach using fundamental linear algebra to describe the GPV maps in terms of a basis for the vector space of Gauss diagrams.","short_abstract":"The linking number and coefficients of the Conway polynomial are two examples of finite type invariants. Goussarov-Polyak-Viro proved that any finite type knot invariant can be computed in a two step process, where the second step is referred to as the GPV map for the invariant. This paper computes the GPV maps for the...","url_abs":"https://arxiv.org/abs/2609.20413","url_pdf":"https://arxiv.org/pdf/2609.20413v1","authors":"[\"Nancy Scherich\",\"Nathaniel Song\"]","published":"2026-09-17T13:57:00Z","proceeding":"math.GT","tasks":"[\"math.GT\"]","methods":"[]","has_code":false}