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Abstract <p> In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and thus determines a finite type invariant of links in the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1163_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\)</EquationSource> </InlineEquation>-sphere. Using the interlace polynomial, we give a lower bound for the size of the Hopf algebra of binary delta-matroids modulo the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10688_2025_1163_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(4\)</EquationSource> </InlineEquation>-term relations. </p>

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The Interlace Polynomial of Binary Delta-Matroids and Link Invariants

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Nadezhda Kodaneva

摘要

Abstract

In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and thus determines a finite type invariant of links in the \(3\) -sphere. Using the interlace polynomial, we give a lower bound for the size of the Hopf algebra of binary delta-matroids modulo the \(4\) -term relations.