Tensor-amplification framework proves equality regularization and spectral equivalence for C-Sidorenko graphs in admissible graphon classes.
On the logarithimic calculus and Sidorenko's conjecture
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abstract
We study a type of calculus for proving inequalities between subgraph densities which is based on Jensen's inequality for the logarithmic function. As a demonstration of the method we verify the conjecture of Erd\"os-Simonovits and Sidorenko for new families of graphs. In particular we give a short analytic proof for a result by Conlon, Fox and Sudakov. Using this, we prove the forcing conjecture for bipartite graphs in which one vertex is complete to the other side.
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Tensor Amplification and Spectral Transfer for Sidorenko-Type Inequalities
Tensor-amplification framework proves equality regularization and spectral equivalence for C-Sidorenko graphs in admissible graphon classes.
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Mathematical exploration and discovery at scale
AlphaEvolve rediscovered best-known solutions for most of 67 tested math problems and found improved solutions in several cases using LLM-guided evolutionary search.