The Miyazawa polynomial for long virtual knots

Atsushi Ishii; Naoko Kamada; Seiichi Kamada

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The Miyazawa polynomial for long virtual knots

机译：宫泽多项式用于长虚拟结

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摘要

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.

机译：我们引入了一个长虚拟结的二变量多项式不变量，该变量主导了闭包的Kauffman f多项式和Miyazawa多项式。我们的不变量满足长虚拟结的串联乘积的乘积公式。它描述了两个虚拟结的“连接和”的宫泽多项式的公式。它还为长的虚拟结的真实交叉数和虚拟交叉数给出了下限。

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来源
《Topology and its applications》 |2010年第1期|290-297|共8页
作者
Atsushi Ishii; Naoko Kamada; Seiichi Kamada;
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作者单位

Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan;

Radiation Effects Research Foundation, Minami-ku, Hiroshima City 732-0815, Japan;

Department of Mathematics, Hiroshima University, Hiroshima 739-8526, Japan;

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正文语种 eng
中图分类
关键词
long virtual knot; miyazawa polynomial; kauffman f-polynomial;

机译：虚长的结宫泽多项式考夫曼f多项式;

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2. THE MIYAZAWA POLYNOMIAL OF PERIODIC VIRTUAL LINKS [J] . JOONOH KIM, SANG YOUL LEE, MYOUNGSOO SEO Osaka Journal of Mathematics . 2009,第3期

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7. The Miyazawa polynomial for long virtual knots [O] . Ishii Atsushi, Kamada Naoko, Kamada Seiichi 2010

机译：宫泽多项式用于长虚拟结

The Miyazawa polynomial for long virtual knots

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