On a Cohen–Lenstra heuristic for Jacobians of random graphs

@article{Clancy2014OnAC,
  title={On a Cohen–Lenstra heuristic for Jacobians of random graphs},
  author={J. Clancy and N. Kaplan and Timothy Leake and S. Payne and M. Wood},
  journal={Journal of Algebraic Combinatorics},
  year={2014},
  volume={42},
  pages={701-723}
}
  • J. Clancy, N. Kaplan, +2 authors M. Wood
  • Published 2014
  • Mathematics
  • Journal of Algebraic Combinatorics
  • In this paper, we make specific conjectures about the distribution of Jacobians of random graphs with their canonical duality pairings. Our conjectures are based on a Cohen–Lenstra-type heuristic saying that a finite abelian group with duality pairing appears with frequency inversely proportional to the size of the group times the size of the group of automorphisms that preserve the pairing. We conjecture that the Jacobian of a random graph is cyclic with probability a little over .7935. We… CONTINUE READING
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