Slavik JABLAN and RADMILA SAZDANOVIĆ |

INTRODUCTION The P-data
(the main input for K2K functions). Instead of a graphical input or
Dowker codes, for the first time in a computer program you can use
human-comprehensive Conway notation of KLs represented as a
Mathematica string and , and not only
with knots. For all work with linksKLs there is no restriction on the number of
crossings. The program provides also the complete data base of alternating
KLs with at most 12 crossings, and non-alternating KLs with
at most 11 crossings, and the database of basic polyhedra with at most 20
crossings. By using LinKnot functions, different symmetry
properties of KLs as a periodicity, amphicheirality, automorphism
groups, or maximum symmetrical projections can be analyzed.
By using
Bernhard-Jablan
. For all alternating ConjectureKLs you can compute
minimum Dowker codes, find all non-isomorphic projections, work with the
graphs of KLs, compute linking numbers, projection gaps, breaking
and splitting numbers, signatures, and many other KL invariants.
The main
property of the program is a possibility to use it as a tool in KLs, for computing properties connected
with infinite classes of KLs (KL families) and make in knot theory. E.g., except the famous Nakanishi-Bleiler
example of a knot 5 1 4 with the unknotting number projection gap, we
discovered an infinite collection of such
new conjecturesKLs. |