Adequacy of link families | Zendy

Slavik Jablan | Zendy; Ljiljana Radović | Zendy; Radmila Sazdanović | Zendy

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Adequacy of link families

Author(s) -

Slavik Jablan,

Ljiljana Radović,

Radmila Sazdanović

Publication year - 2010

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1002021j

Subject(s) - link (geometry) , notation , invariant (physics) , polynomial , mathematics , discrete mathematics , computer science , algebra over a field , combinatorics , pure mathematics , arithmetic , mathematical analysis , mathematical physics

Using computer calculations and working with representatives of pretzel tangles we established general adequacy criteria for different classes of knots and links. Based on adequate graphs obtained from all Kauffman states of an alternating link we defined a new numerical invariant: adequacy number, and computed adequacy polynomial which is the invariant of alternating link families. Adequacy polynomial distinguishes (up to mutation) all families of alternating knots and links whose generating link has at most $n=12$ crossings.

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