Adequacy of Link Families

Slavik Jablan, Ljiljana Radović, Radmila Sazdanović

We analyze adequacy of knots and links, utilizing Conway notation, Montesinos tangles and {t Linknot} and {t KhoHo} computer calculations. We introduce a numerical invariant called adequacy number, and compute adequacy polynomial which is the invariant of alternating link families. According to computational results, adequacy polynomial distinguishes (up to mutation) all families of alternating knots and links generated by links with at most 12 crossings.