All-orders asymptotics of tensor model observables from symmetries of restricted partitions

@article{BenGeloun2022AllordersAO,
  title={All-orders asymptotics of tensor model observables from symmetries of restricted partitions},
  author={Joseph Ben Geloun and Sanjaye Ramgoolam},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2022},
  volume={55}
}
The counting of the dimension of the space of U(N)×U(N)×U(N) polynomial invariants of a complex 3-index tensor as a function of degree n is known in terms of a sum of squares of Kronecker coefficients. For n⩽N , the formula can be expressed in terms of a sum of symmetry factors of partitions of n denoted Z3(n) , which also counts the number of bipartite ribbon graphs with n edges. We derive the large n all-orders asymptotic formula for Z3(n) making contact with high order results previously… 

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