of some programs which can be used to calculate the Fiedler solid torus invariants, generate PostScript images of knots, links, and tangles (1/10 in size of those rendered by KnotScape and 1/100 of those rendered by the Adobe Illustrator), and convert between different formats (including the one of KnotScape's editor).
More information on what the programs do and instructions how they are to be used may be found in the paper
The test messages what is computed compare well (not perfectly) to this version of the paper.
Program aqv23tst7.C is for crossings (though it was updated to subsume the step of Jones polynomial calculation explained in the paper). Programs aqv23tst8*.C are for crossings.
Compiling with g++ on UNIX and calling the program without any argument should work (though some programs give no output, because there are no diagrams of the sought type). There are some comments in the programs, but better let me know if you like to try them out. So far I give no detailed explanation, since I'm not sure who will be interested...
alpha_bd.m, and almax_bd_7a.m, two data files which can be read in from the notebook file to avoid the most time consuming parts of the calculation.
h2br_m2.pdf and h2br_m2.ps.gz, printouts of the MATHEMATICA notebook (with full graphics). PS is compressed because it's 63M.
h2br3a.ps and h2br3a.pdf, draft of the paper, not in publication-ready form, but with full explanation of all details of the calculation. Comments in the MATHEMATICA notebook refer to this draft.
contains a program illustrating the calculation of the number of non-isomorphic knot markings of graphs (per convention in this section always 3-connected planar cubic, unless stated otherwise), which gives the number of maximal knot generators by crossing number. The archive is supplemented with data for genus 5. It contains the following files.
markgs <gr_file> <aut_file>where gr_file: is a file of 3-valent 3-connected planar graphs and aut_file contains data of their automorphisms (format see below).
Note that for generators of genus g one needs n=4*g-2 vertices.
markgs tri.18.g tri.18.aut2
gawk -f asc2math.awk tri.18 | sed 's/[^0-9][^0-9]*/ /g' > tri.18.gto move the plantri format of graphs to one where each graph of n vertices is encoded by a sequence of 3*n integers, with each triplet giving the vertices adjacent to a given vertex 1,...,n in cyclic order of the (unique!) planar embedding. The sequence of 3*n integers is preceded by n (the number of vertices) and an integer id.
The file tri.18.aut2 contains the automorphisms of the graphs in tri.18, with each line standing for one graph. The line starts with a non-negative integer s, which means that the automorphism group has order s+1. (The trivial automorphism is always discarded.) Then there is a sequence of s*n integers, with each subsequence of length n being the permutation of the n vertices of each non-trivial automorphism. These automorphisms were generated with MATHEMATICA.
The first entry in the vectors of tri.18.stat corresponds to maximal generators of crossing number 6*g-3(=27), and such do not occur here (albeit they do occur for g≥6). The last entry in the vectors corresponds to crossing number 10*g(-6)=44, and is also always 0 (for every g). There is a single graph where the vector is 0, i.e., there are no knot markings at all. (This graph is called B3 in the paper.)
The archive further features:
gr2dt < tri.18.g > tri.18.ken
plantri -a -d 19 -c4 | head | perl -f asc2math2x.prl2 | cat -n | markgs_X4f5cand you should get
34 1 3 19 59024 0 -42732 0 -11966 0 -25044 0 16510 0 3734 0 436 0 36 0 2 34 2 3 19 62592 0 -50976 0 5992 0 -35202 0 13578 0 3554 0 424 0 36 0 2 34 3 3 19 -12128 0 7696 0 14930 0 -30664 0 15180 0 4430 0 512 0 42 0 2 34 4 3 19 15904 0 -8720 0 4466 0 -31588 0 15252 0 4142 0 500 0 42 0 2 34 5 3 19 17888 0 -59312 0 77854 0 -49428 0 9044 0 3474 0 440 0 38 0 2 34 6 3 19 21952 0 -29072 0 38920 0 -46128 0 10372 0 3494 0 422 0 38 0 2 34 7 3 19 44384 0 -68648 0 20508 0 -18938 0 18048 0 4136 0 470 0 38 0 2 34 8 3 19 40736 0 29088 0 -51298 0 -40782 0 17212 0 4486 0 514 0 42 0 2 34 9 3 19 -89824 0 6672 0 85010 0 -22074 0 15484 0 4186 0 502 0 42 0 2 34 10 3 19 15536 0 8964 0 6204 0 -44626 0 10312 0 3184 0 388 0 36 0 2 ended at 34 10which are the slN polynomials of plantri's first 10 cubic planar c4c graphs with χ=-17.
NOTE: the input format is as above, cyclic ordering of adjacent vertices, but this program works also for non-planar graphs!
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