Link lengths and their growth powers

Title
Link lengths and their growth powers
Authors
허영식
Keywords
minimum lattice length; ropelength; stick number
Issue Date
2015-01
Publisher
IOP PUBLISHING LTD
Citation
Journal of Physics A: Mathematical and Theoretical. 48(3) 035202(1-10)
Abstract
For a certain infinite family f of knots or links, we study the growth power ratios of their stick number, lattice stick number, minimum lattice length and minimum ropelength compared with their minimum crossing number c(K) for every K is an element of f. It is known that the stick number and lattice stick number grow between the 1/2 and linear power of the crossing number, and minimum lattice length and minimum ropelength grow with at least the 3/4 power of crossing number (which is called the four-thirds power law). Furthermore, the minimal lattice length and minimum ropelength grow at most as O(c(K)[ln(c(K))](5)), but it is unknown whether any family exhibits superlinear growth. For any real number r between 1/2 and 1, we give an infinite family of non-splittable prime links in which the stick number and lattice stick number grow exactly as the rth power of crossing number. Furthermore for any real number r between 3/4 and 1, we give another infinite family of non-splittable prime links in which the minimum lattice length and minimum ropelength grow exactly as the rth power of crossing number.
URI
http://hdl.handle.net/20.500.11754/21141http://iopscience.iop.org/article/10.1088/1751-8113/48/3/035202/meta;jsessionid=55AFAC61D3FF522A07CE02B54317CD11.c2.iopscience.cld.iop.org
ISSN
1751-8113
DOI
http://dx.doi.org/10.1088/1751-8113/48/3/035202
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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