# Solving Turán's Tetrahedron Problem for the $\ell_2$-Norm

## József Balogh, Felix Christian Clemen, Bernard Lidický

This page is containing computer assisted parts of the paper titled
*Solving Turán's Tetrahedron Problem for the $\ell_2$-Norm*.
A preliminary version of the paper can be downloaded here.

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*
The archive contains three subdirectoris `codegreesquared_F33`, `codegreesquared_K4`, and `codegreesquared_K5` and each contains data for one calculation. Below we provide description of files that appear in the main directory and subdirectories.

` rounding_exact.sage ` ... shared Sage providing tools for rounding semidefinite program
` F_3edges__forbidden.txt ` ... list of forbidden (induced) subgraphs
` F_3edges__n6_labeled.txt ` ... list of labeled 3-graphs on 6 vertices used in the calculation
` F_3edges__n6_unlabeled.txt ` ... list of all 3-graphs on up to 6 vertices
` F_3edges__objective.txt ` ... Function to optimize - sum of codegree squared
` Makefile ` ... for building the program creading semidefinite program
` SDP_n6_UB_F_3edges__objective.txt.dat-s ` ... semidefinite program - input to csdp
` SDP_n6_UB_F_3edges__objective.txt.dat-s.result ` ... numerical solution from csdp
` altered*.dat-s ` ... projection of the semidefinite program
` altered*.dat-s.result ` ... numerical solution projection of the semidefinite program from csdp
` altered*.dat-s.linear_solution.sage ` ... rational solution - this is the actual solution - certificate for the actual proof
` round.sage ` ... script for rounding `SDP_n6_UB_F_3edges__objective.txt.dat-s` into `altered*.dat-s.linear_solution.sage`
` run.sh ` ... shell script to run the entire process
` transcript.txt ` ... output of run.sh