Phase transitions in number theory: from the birthday problem to Sidon sets.

@article{Luque2013PhaseTI,
  title={Phase transitions in number theory: from the birthday problem to Sidon sets.},
  author={Bartolo Luque and Ivan Gonzalez Torre and Lucas Lacasa},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={88 5},
  pages={
          052119
        }
}
In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in… CONTINUE READING

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