This page contains computer assisted parts of the paper On the crossing numbers of complete graphs.

A preliminary version of the paper can be downloaded here or from arXiv.

Here, you can download the technical things as one archive

- hill_computations.zip (zip, around 0.5MB)
- hill_computations_2.zip (zip, around 200MB, includes some generated files)
- hill3.tar.gz (tar.gz, around 285MB, includes all generated files and some transcripts of execution)

* Dependencies*

* Description of the content
*

`Makefile.include`... Common part of Makefile for all calculations.`flag.cpp`... C++ program that calculates coefficients in the semidefinite program`rounding_Integer.sage`... Sage script to perform approximate rounding of solutions of semidefinite program by CSDP.`*/run.sh`... script to perform the entire calculation (uncomment sections as needed)`*/Makefile`... for compilation of`flag.cpp``*/F_rotationsystem*__objective.txt`... $N_4$, the rotations on 4 vertices without crossing, with different scale`*/SDP_n*.dat-s`... semidefinite program for calculating upper bound for $\phi(N_4)$ (generated file)`*/SDP_n*.dat-s.result`... Solution to the semidefinite program using CSDP (generated file)`*/SDP_n*.pkl`... Rounded matrices from CSDP (generated file - the actual certificates of a proof)`rotation_systems/F_rotationsystem__n5_unlabeled.txt`... $\mathcal{E}_1,\ldots,\mathcal{E}_5$ rotations on up to 5 vertices`rotation_systems/F_rotationsystem__n7_labeled.txt`... Labeled flags $F_1,\ldots,F_8$ (generated file)`rotation_systems/F_rotationsystem__n7_unlabeled.txt`... $\mathcal{E}_1,\ldots,\mathcal{E}_7$ rotations on up to 7 vertices (generated file)`rotation_systems_convex/F_rotationsystem__n5_unlabeled.txt`... $\mathcal{C}_1,\ldots,\mathcal{C}_5$ convex rotations on up to 5 vertices`rotation_systems_convex/F_rotationsystem__n8_labeled.txt`... Labeled flags $F_1,\ldots,F_5$ (generated file)`rotation_systems_convex/F_rotationsystem__n8_unlabeled.txt`... $\mathcal{C}_1,\ldots,\mathcal{C}_8$ convex rotations on up to 8 vertices`rotation_systems_blind/*`... Not used in the paper, included for curious readers`rotation_systems_blind/F_rotationsystemblind__n5_unlabeled.txt`... $\mathcal{M}_1,\ldots,\mathcal{M}_5$ rotations on up to 5 vertices`rotation_systems_blind/F_rotationsystemblind__n7_labeled.txt`... possible labeled flags for calculation. (generated file)`rotation_systems_blind/F_rotationsystemblind__n7_unlabeled.txt`... $\mathcal{M}_1,\ldots,\mathcal{M}_7$ rotations on up to 7 vertices (generated file)`rotation_systems_convex_blind/*`... Not used in the paper, included for curious readers`rotation_systems_convex_blind/F_rotationsystemblind__n5_unlabeled.txt`... convex rotations on up to 5 vertices from $\mathcal{M}_1,\ldots,\mathcal{M}_5$`rotation_systems_convex_blind/F_rotationsystemblind__n8_labeled.txt`... possible labeled flags for calculation. (generated file)`rotation_systems_convex_blind/F_rotationsystemblind__n8_unlabeled.txt`... convex rotations on up to 8 vertices from $\mathcal{M}_1,\ldots,\mathcal{M}_8$ (generated file)