6 papers
Erdős-Ko-Rado properties of Steiner 2-designs
Sam Adriaensen, Sergey Goryainov, Elena V. Konstantinova +1
In this paper, we prove an Erdős-Ko-Rado characterisation of maximum intersecting families of blocks in Steiner -designs arising from Desarguesian maximal arcs. This answers a r…
CayleyPy-4: AI-Holography. Towards analogs of holographic string dualities for AI tasks
A. Chervov, F. Levkovich-Maslyuk, A. Smolensky +41
This is the fourth paper in the CayleyPy project, which applies AI methods to the exploration of large graphs. In this work, we suggest the existence of a new discrete version of h…
Thin divisible designs graphs: an interplay between fixed-point free involutions of -graphs and symmetric weighing matrices
Sergey Goryainov, Willem H. Haemers, Elena V. Konstantinova +1
In this paper, we illustrate important aspects of the interplay between weighing matrices, -graphs with fixed-point free involutions, and signed graphs with an orthogonal…
Generating the symmetric group by three prefix reversals
Saúl A. Blanco, Mikhail P. Golubyatnikov, Elena V. Konstantinova +2
The cubic pancake graphs are Cayley graphs over the symmetric group generated by three prefix reversals. There is the following open problem: characterize all the…
CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)
A. Chervov, D. Fedoriaka, E. Konstantinova +46
This is the third paper of the CayleyPy project applying artificial intelligence to problems in group theory. We announce the first public release of CayleyPy, an open source Pytho…
Non-canonical maximum cliques without a design structure in the block graphs of 2-designs
Sergey Goryainov, Elena V. Konstantinova
In this note we answer positively a question of Chris Godsil and Karen Meagher on the existence of a 2-design whose block graph has a non-canonical maximum clique without a design…