Central and Local Limit Theorems Applied to Asymptotic Enumeration. III. Matrix Recursions

@article{Bender1983CentralAL,
  title={Central and Local Limit Theorems Applied to Asymptotic Enumeration. III. Matrix Recursions},
  author={Edward A. Bender and L. Bruce Richmond and S. Gill Williamson},
  journal={J. Comb. Theory, Ser. A},
  year={1983},
  volume={35},
  pages={263-278}
}
Abstract Let a multivariate sequence an(k) be obtained by a matrix recursion. It is shown that it is usually easy to establish central and local limit theorems for an(k). The proof requires a lemma on multisection of multivariate series which appears to be new. The applications of the limit theorems include covering by polyominoes, enumeration of plane animals, occupancy problems, 0–1 matrices, and nonexistence of critical phenomena. 

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