Geodesic
Classification of knots in a thickened torus with minimal octahedron diagrams which are not contained in an annulus
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 1, pp. 5-10

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The aim of this research is to tabulate knots in a thickened torus $\mathrm{T\times I}$ having minimal diagrams which are not contained in an annulus and correspond to the octahedron graph. Tabulation consists of three steps. First, a table of knot projections on $\mathrm{I}$ was compiled. Then, every projection was converted into a set of corresponding diagrams. Finally, using a generalized version of the Kauffman bracket as an invariant, duplicates were removed and all the knots obtained were proved to be different.
Keywords: knot; thickened torus; knot table. 
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     title = {Classification of knots in a thickened torus with minimal octahedron diagrams which are not contained in an annulus},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
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     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2015_7_1_a0/}
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A. A. Akimova. Classification of knots in a thickened torus with minimal octahedron diagrams which are not contained in an annulus. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 1, pp. 5-10. http://geodesic.mathdoc.fr/item/VYURM_2015_7_1_a0/