Реферат: In this talk we review some new results obtained by using AI methods to check open problems in Cayley graph theory and to state new conjectures. The results discussed in the talk are published in [ https://doi.org/10.48550/arXiv.2509.19162]. This is the third paper of the CayleyPy project applying artificial intelligence methods to problems in group theory. This is the first paper where the public release of CayleyPy is announced. CayleyPy is an open-source Python library for computations with Cayley and Schreier graphs. Compared with state-of-the-art systems based on classical methods, such as GAP and Sage, CayleyPy handles significantly larger graphs and performs several orders of magnitude faster. For many Cayley graphs over the symmetric group quasi--polynomial diameter formulas are observed: a small set of quadratic or linear polynomials, and it is conjectured that it is a general phenomenon. These lead to efficient diameter computation, despite the problem being NP-hard in general, and to new conjectures. Some of conjectures are LLM-friendly - they can be stated as sorting problems, which are easy to formulate for LLM, and their solutions can be given by an algorithm or by a Python code, which is easy to verify, so they can be used to test LLM's abilities to solve research problems. To benchmark various methods of path-finding on Cayley graphs more than 10 benchmark datasets were created in the form of Kaggle challenges, making benchmarking easy and public to the community. CayleyPy works with arbitrary permutation or matrix groups, and supports a pre-defined collection of more than a hundred generators including puzzle groups. The code for direct growth computation outperforms similar functions on the standard computer algebra system GAP/SAGE up to 1000 times both in speed and in maximum sizes of the graphs that it can handle.

Библиографическая ссылка: Konstantinova E.
Artificial intelligence methods for Cayley graphs
Probability Techniques in Analysis and Approximation Theory 24-29 Nov 2025