Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Jin, Gyo Taek"'
Autor:
Jin, Gyo Taek, Kim, Hun, Kim, Minchae, Lee, Hwa Jeong, Ryu, Songwon, Shin, Dongju, Stoimenow, Alexander
There are 46,972 prime knots with crossing number 14. Among them 19,536 are alternating and have arc index 16. Among the non-alternating knots, 17, 477, and 3,180 have arc index 10, 11, and 12, respectively. The remaining 23,762 have arc index 13 or
Externí odkaz:
http://arxiv.org/abs/2407.15859
A knot is a closed loop in space without self-intersection. Two knots are equivalent if there is a self homeomorphism of space bringing one onto the other. An arc presentation is an embedding of a knot in the union of finitely many half planes with a
Externí odkaz:
http://arxiv.org/abs/2406.15361
We give a list of minimal grid diagrams of the 13 crossing prime nonalternating knots which have arc index 13. There are 9,988 prime knots with crossing number 13. Among them 4,878 are alternating and have arc index 15. Among the other nonalternating
Externí odkaz:
http://arxiv.org/abs/2402.02717
Autor:
Lee, Hwa Jeong, Jin, Gyo Taek
Let $r$ be an odd integer, $r\ge3$. Then the petal number of the torus knot of type $(r,r+2)$ is equal to $2r+3$.
Comment: 6 pages, 7 figures
Comment: 6 pages, 7 figures
Externí odkaz:
http://arxiv.org/abs/2112.13211
Autor:
Jin, Gyo Taek, Lee, Hwa Jeong
In this article, we give a list of minimal grid diagrams of the 12 crossing prime alternating knots. This is a continuation of the work in https://doi.org/10.1142/S0218216520500765
Comment: 20 pages, 2 figures, 1288 grid diagrams, submitted to t
Comment: 20 pages, 2 figures, 1288 grid diagrams, submitted to t
Externí odkaz:
http://arxiv.org/abs/2012.14269
As a continuation of the previous works to tabulate the prime knots up to arc index 11, we provide the list of prime knots with arc index 12 up to 16 crossings and their minimal grid diagrams. There are 19,513 prime knots of arc index 12 up to 16 cro
Externí odkaz:
http://arxiv.org/abs/2007.05711
Autor:
Jin, Gyo Taek, Lee, Ho
For the alternating knots or links, mutations do not change the arc index. In the case of nonalternating knots, some semi-alternating knots or links have this property. We mainly focus on the problem of mutation invariance of the arc index for nonalt
Externí odkaz:
http://arxiv.org/abs/1704.01787
Autor:
Lee, Hwa Jeong, Jin, Gyo Taek
We computed the arc index for some of the pretzel knots $K=P(-p,q,r)$ with $p,q,r\ge2$, $r\geq q$ and at most one of $p,q,r$ is even. If $q=2$, then the arc index $\alpha(K)$ equals the minimal crossing number $c(K)$. If $p\ge3$ and $q=3$, then $\alp
Externí odkaz:
http://arxiv.org/abs/1204.0597
Autor:
Jin, Gyo Taek, Lee, Hwa Jeong
It is known that the arc index of alternating knots is the minimal crossing number plus two and the arc index of prime nonalternating knots is less than or equal to the minimal crossing number. We study some cases when the arc index is strictly less
Externí odkaz:
http://arxiv.org/abs/1106.2723
Autor:
Jin, Gyo Taek, Park, Wang Keun
Every knot can be embedded in the union of finitely many half planes with a common boundary line in such a way that the portion of the knot in each half plane is a properly embedded arc. The minimal number of such half planes is called the arc index
Externí odkaz:
http://arxiv.org/abs/1010.3005