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Mathematics > Combinatorics
Title: Constructions in combinatorics via neural networks
(Submitted on 29 Apr 2021)
Abstract: We demonstrate how by using a reinforcement learning algorithm, the deep cross-entropy method, one can find explicit constructions and counterexamples to several open conjectures in extremal combinatorics and graph theory. Amongst the conjectures we refute are a question of Brualdi and Cao about maximizing permanents of pattern avoiding matrices, and several problems related to the adjacency and distance eigenvalues of graphs.
Submission history
From: Adam Zsolt Wagner [view email][v1] Thu, 29 Apr 2021 17:32:56 GMT (1415kb,D)
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