minimal lattice
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Author(s):  
Marion Campisi ◽  
Nicholas Cazet
Keyword(s):  

The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the [Formula: see text]-norm. Inspired by Gromov, Pardon and Blair–Campisi–Taylor–Tomova, we show that results about the distortion of smooth knots hold for vertex distortion: the vertex distortion of a lattice knot is 1 only if it is the unknot, and there are minimal lattice-stick number knot conformations with arbitrarily high distortion.


Nature ◽  
2017 ◽  
Vol 544 (7651) ◽  
pp. 460-464 ◽  
Author(s):  
Suihe Jiang ◽  
Hui Wang ◽  
Yuan Wu ◽  
Xiongjun Liu ◽  
Honghong Chen ◽  
...  

2014 ◽  
Vol 1040-1041 ◽  
pp. 167-176 ◽  
Author(s):  
Jan Wahl ◽  
Robert Binder ◽  
Irene Burghardt

2013 ◽  
Vol 46 (14) ◽  
pp. 5724-5730 ◽  
Author(s):  
P. Knychała ◽  
M. Dzięcielski ◽  
M. Banaszak ◽  
N. P. Balsara

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1357-1372 ◽  
Author(s):  
Vasilios Katsikis

In this paper the notion of strongly resolving markets with respect to the positive basis of a minimal lattice-subspace Y of Rm is defined. It is proved that if the number of securities is less than half the dimension of Y, then not a single (non-trivial) option can be replicated. This result extends already known results regarding the notion of a market being strongly resolving. Both theoretical and computational methods are provided in order to establish criteria for the characterization of markets that do not replicate any option.


2012 ◽  
Vol 2012 (05) ◽  
pp. P05003 ◽  
Author(s):  
E J Janse van Rensburg ◽  
A Rechnitzer
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