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The Miyazawa polynomial for long virtual knots |
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| Authors: | Atsushi Ishii Naoko Kamada Seiichi Kamada |
| Institution: | aInstitute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan;bRadiation Effects Research Foundation, Minami-ku, Hiroshima City 732-0815, Japan;cDepartment of Mathematics, Hiroshima University, Hiroshima 739-8526, Japan |
| Abstract: | We introduce a two-variable polynomial invariant of a long virtual knot, which dominates the Kauffman f-polynomial and the Miyazawa polynomial of the closure. Our invariant satisfies a product formula for the concatenation product of long virtual knots. It describes a formula of the Miyazawa polynomial of a ‘connected sum’ of two virtual knots. It also gives lower bounds for the real crossing number and the virtual crossing number of a long virtual knot. |
| Keywords: | Long virtual knot Miyazawa polynomial Kauffman f-polynomial |
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