Asymptotic enumeration of lonesum matrices

@article{Khera2021AsymptoticEO,
  title={Asymptotic enumeration of lonesum matrices},
  author={Jessica Khera and Erik Lundberg and Stephen Melczer},
  journal={Adv. Appl. Math.},
  year={2021},
  volume={123},
  pages={102118}
}
We provide asymptotics for the poly-Bernoulli numbers, a combinatorial array that enumerates lonesum matrices. We obtain these (bivariate) asymptotics as an application of ACSV (Analytic Combinatorics in Several Variables). For the diagonal asymptotic (i.e., for the special case of square lonesum matrices) we present an alternative proof based on Parseval's identity. We also strengthen an existing result on asymptotic enumeration of permutations having a specified excedance set. 
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References

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