|School:||Faculty of Mathematics and Physics, Charles University, Prague|
|Project:||Antipodal monochromatic paths in hypercubes|
|Coworkers:||Tung Anh Vu, Marian Poljak|
The first week was a bit slow from my part. But we have managed to make a great presentation (even stylistically). The next week the real work will begin. Our team has agreed on regular meetings in Prague and firstly we start with deep exploration of small hypercubes e.g. Q_4 (similar to what Vojtěch Dvořák did).
We had two meeting of our team. At the first one, we discussed thing more in general perpestive and were maily exploring the field without any concrete work.
At the second one, we start off with solving loads of various question 'just to get into that'. It was probably also not extremely productive, but it was great to actually do something more than just reading papers.
This week we continued our work on small cubes and we have our first small results. The proofs was primarily based on comupter calculations and but we tried to justify the results from human point of view (with partial success).
On week 4 we again work with small cubes (dimension 4 and 5) but we also aim on more general question and we has a few results there. But to our disappointment we discowered that those statements was proved before.
This work was carried out while the author Tomáš Hons was a participant in the 2020 DIMACS REU program, supported by CoSP, a project funded by European Union’s Horizon 2020 research and innovation programme, grant agreement No. 823748.