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Mathematics > Combinatorics

arXiv:2104.14516 (math)
[Submitted on 29 Apr 2021]

Title:Constructions in combinatorics via neural networks

Authors:Adam Zsolt Wagner
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    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.

Comments: 23 pages, 13 figures
Subjects: Combinatorics (math.CO); Machine Learning (cs.LG)
Cite as:  arXiv:2104.14516 [math.CO]
          (or arXiv:2104.14516v1 [math.CO] for this version)

Submission history

From: Adam Zsolt Wagner [view email]
[v1] Thu, 29 Apr 2021 17:32:56 UTC (1,415 KB)
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