A two-variable polynomial invariant of virtual knots

被引：0
|
作者：
Jeong, Myeong-Ju [1 ]
机构：
[1] Korea Adv Inst Sci & Technol, Dept Math & Comp Sci, Korea Sci Acad, 111 Baekyang, Busan 47162, South Korea
来源：
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2023年 / 32卷 / 13期
关键词：
Virtual knot; affine index polynomial; writhe polynomial; crossing change; GORDIAN DISTANCE;
D O I：
10.1142/S0218216523500955
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce a polynomial invariant of virtual knots by using weights of crossings. It is motivated from the writhe polynomial and the affine index polynomial for virtual knots. The new polynomial invariant is distinct from these polynomials and is a Vassiliev invariant of degree 1. By using the polynomial invariant we give a lower bound for the Gordian distance of two homotopic virtual knots.
引用
收藏
页数：19
相关论文
共 50 条
  • [21] On the computation of the inverse of a two-variable polynomial matrix by interpolation
    Karampetakis, Nicholas P.
    Evripidou, Alexandros
    [J]. MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING, 2012, 23 (1-2) : 97 - 118
  • [22] A two-variable approach to solve the polynomial Lyapunov equation
    Peeters, R
    Rapisarda, P
    [J]. SYSTEMS & CONTROL LETTERS, 2001, 42 (02) : 117 - 126
  • [23] A two-variable approach to solve the polynomial Lyapunov equation
    Peeters, R
    Rapisarda, P
    [J]. PROCEEDINGS OF THE 39TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5, 2000, : 2504 - +
  • [24] Generalized inverses of two-variable polynomial matrices and applications
    N. P. Karampetakis
    [J]. Circuits, Systems and Signal Processing, 1997, 16 : 439 - 453
  • [25] Polynomial Generalizations of two-variable Ramanujan type identities
    Mc Laughlin, James
    Sills, Andrew V.
    [J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2011, 18 (02):
  • [26] On the computation of the inverse of a two-variable polynomial matrix by interpolation
    Nicholas P. Karampetakis
    Alexandros Evripidou
    [J]. Multidimensional Systems and Signal Processing, 2012, 23 : 97 - 118
  • [27] A POLYNOMIAL INVARIANT OF KNOTS AND LINKS
    HOSTE, J
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 1986, 124 (02) : 295 - 320
  • [28] Two-variable Hermite Polynomial State and Its Wigner Function
    Xiang-Guo Meng
    Ji-Suo Wang
    Bao-Long Liang
    [J]. International Journal of Theoretical Physics, 2009, 48 : 3268 - 3277
  • [29] The algorithm for computing the Drazin inverses of two-variable polynomial matrices
    Bu, FB
    Wei, YM
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2004, 147 (03) : 805 - 836
  • [30] Two-variable Hermite Polynomial State and Its Wigner Function
    Meng, Xiang-Guo
    Wang, Ji-Suo
    Liang, Bao-Long
    [J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2009, 48 (11) : 3268 - 3277
12345