caa a22 4500 445855487 CHVBK 20180317145426.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00026-011-0087-4 doi (NATIONALLICENCE)springer-10.1007/s00026-011-0087-4 Moffatt Iain Department of Combinatorics and Optimization, University of Waterloo, 200 University Avenue, West Waterloo, Ontario, Canada aut Unsigned State Models for the Jones Polynomial [Elektronische Daten] [Iain Moffatt] It is a well-known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we show that for every diagram of a link in S 3 there exists a diagram of an alternating link in a thickened surface (and an alternating virtual link) with the same Kauffman bracket. We also recover two recent results in the literature relating to the Jones and Bollobás-Riordan polynomials and show they arise from two different interpretations of the same embedded graph. Springer Basel AG, 2011 Bollobás-Riordan polynomial nationallicence embedded graphs nationallicence Jones polynomial nationallicence medial graph nationallicence Potts model nationallicence ribbon graphs nationallicence vertex model nationallicence Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 127-146 0218-0006 15:1<127 2011 15 26 https://doi.org/10.1007/s00026-011-0087-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00026-011-0087-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Moffatt Iain Department of Combinatorics and Optimization, University of Waterloo, 200 University Avenue, West Waterloo, Ontario, Canada aut NATIONALLICENCE 773 0- Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 127-146 0218-0006 15:1<127 2011 15 26 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer