503 research outputs found
Mirror-Curves and Knot Mosaics
Inspired by the paper on quantum knots and knot mosaics [23] and grid
diagrams (or arc presentations), used extensively in the computations of
Heegaard-Floer knot homology [2,3,7,24], we construct the more concise
representation of knot mosaics and grid diagrams via mirror-curves. Tame knot
theory is equivalent to knot mosaics [23], mirror-curves, and grid diagrams
[3,7,22,24]. Hence, we introduce codes for mirror-curves treated as knot or
link diagrams placed in rectangular square grids, suitable for software
implementation. We provide tables of minimal mirror-curve codes for knots and
links obtained from rectangular grids of size 3x3 and px2 (p<5), and describe
an efficient algorithm for computing the Kauffman bracket and L-polynomials
[18,19,20] directly from mirror-curve representations
Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory
This paper is a concise introduction to virtual knot theory, coupled with a
list of research problems in this field.Comment: 65 pages, 24 figures. arXiv admin note: text overlap with
arXiv:math/040542
Meteorological interpretation of Nimbus High Resolution Infrared /HRIR/ data
Nimbus satellite high resolution infrared photographic data analysi
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