Maximum Number of Almost Similar Triangles in the Plane
József Balogh, Felix Christian Clemen, Bernard Lidický
This page is containing computer assisted parts of the paper titled
Maximum Number of Almost Similar Triangles in the Plane.
A preliminary version of the paper can be downloaded here
or from arxiv.
You can download the technical things as one archive
Other (pre)requisites for redoing the entire calculation
Sage Math for transforming numerical solution to an rational solution - getting an actual proof
C++ compiled on MacOSX or Linux rebuilding the program for creating semidefinite program
CSDP solved for semidefinite programs
Description of the files in anc.zip
- rounding_Integer.sage ... shared Sage providing tools for rounding semidefinite program
- F_3edges__n7_labeled.txt ... list of labeled 3-graphs on 8 vertices used in the calculation
- F_3edges__n7_unlabeled.txt ... list of all 3-graphs on up to 8 vertices
- F_3edges__forbidden.txt ... list of forbidden (induced) subgraphs
- F_3edges__n8_labeled.txt ... list of labeled 3-graphs on 8 vertices used in the calculation
- F_3edges__n8_unlabeled.txt ... list of all 3-graphs on up to 8 vertices
- F_3edges__objective.txt ... Function to optimize: t_1,1,1 = just edge edensity
- F_3edges__objective_221.txt ... Function to optimize: t_2,2,1
- F_3edges__objective_combined.txt ... Function to optimize: 3*t_3,3,1 + 3.5*t_3,2,2 - t_4,2,1
- Makefile ... for building the program creading semidefinite program
- SDP_n7_UB_F_3edges__objective_221.txt.dat-s ... semidefinite program for t_2,2,1
- SDP_n7_UB_F_3edges__objective_221.txt.dat-s.log ... output of CSDP when solving the program
- SDP_n7_UB_F_3edges__objective_221.txt.dat-s.result ... numerical solution generated by CSDP
- SDP_n7_UB_F_3edges__objective_221.txt.dat-s.result.rounded.Integer.all.pkl ... rational (exact) solution
- SDP_n8_LB_F_3edges__objective_combined.txt.dat-s ... semidefinite program for the combined function
- SDP_n8_LB_F_3edges__objective_combined.txt.dat-s.log ... output of CSDP when solving the program
- SDP_n8_LB_F_3edges__objective_combined.txt.dat-s.result .. numerical solution
- SDP_n8_LB_F_3edges__objective_combined.txt.dat-s.result.rounded.Integer.all.pkl ... rational solution (exact)
- filter.py ... python script for testing if a 3-graph is forbidden or not
- flag.cpp ... C++ program for generating the semidefinite programs
- rounding.log ... output of rounding.sage
- rounding.sage ... rounding procedure for SDP_n8_LB_F_3edges__objective_combined.txt.dat-s
- rounding.small.221.log ... output of rounding.small.221.sage
- rounding.small.221.sage ... rounding procedure for SDP_n8_LB_F_3edges__objective_combined.txt.dat-s
- rounding_Integer.sage ...common functions for rounding semidefinite program