Minimal diagrams of free knots
2014 ◽
Vol 23
(06)
◽
pp. 1450032
Manturov recently introduced the idea of a free knot, i.e. an equivalence class of virtual knots where equivalence is generated by crossing change and virtualization moves. He showed that if a free knot diagram is associated to a graph that is irreducibly odd, then it is minimal with respect to the number of classical crossings. Not all minimal diagrams of free knots are associated to irreducibly odd graphs, however. We introduce a family of free knot diagrams that arise from certain permutations that are minimal but not irreducibly odd.
2020 ◽
Vol 29
(02)
◽
pp. 2040004
◽
Keyword(s):
2017 ◽
Vol 26
(13)
◽
pp. 1750090
Keyword(s):
2013 ◽
Vol 22
(13)
◽
pp. 1350073
◽
Keyword(s):
2006 ◽
Vol 15
(03)
◽
pp. 327-338
◽
2014 ◽
Vol 23
(06)
◽
pp. 1450031
◽
Keyword(s):
2015 ◽
Vol 24
(08)
◽
pp. 1550046
2011 ◽
Vol 20
(08)
◽
pp. 1173-1215
2002 ◽
Vol 11
(03)
◽
pp. 311-322
◽
Keyword(s):