• DOI:10.1016/S0012-365X(00)00373-3
Corpus ID: 44620783

Recursively defined combinatorial functions: extending Galton's board

@article{Neuwirth2001RecursivelyDC,
  title={Recursively defined combinatorial functions: extending Galton's board},
  author={E. Neuwirth},
  journal={Discret. Math.},
  year={2001},
  volume={239},
  pages={33-51}
}

E. Neuwirth

Published 2001

Computer Science, Mathematics

Discret. Math.

Abstract Many functions in combinatorics follow simple recursive relations of the type F(n,k)=an−1,kF(n−1,k)+bn−1,k−1F(n−1,k−1). Treating such functions as (infinite) triangular matrices and calling an,k and bn,k generators of F, our paper will study the following question: Given two triangular arrays and their generators, how can we give explicit formulas for the generators of the product matrix? Our results can be applied to factor infinite matrices with specific types of generators (e.g. an… CONTINUE READING

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