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math.CO2026
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…
math.CO2025
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…
math.CO2025
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…