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
    23 Citations

    Figures and Topics from this paper

    Explore Further: Topics Discussed in This Paper

    A combinatorial approach to a general two-term recurrence
    • 6
    • Highly Influenced
    • PDF
    Recurrent Combinatorial Sums and Binomial-Type Theorems
    • Highly Influenced
    • PDF
    Bivariate generating functions for a class of linear recurrences: General structure
    • 15
    • PDF
    On Solutions to a General Combinatorial Recurrence
    • 11
    • Highly Influenced
    • PDF
    ELA CERTAIN MATRICES RELATED TO THE FIBONACCI SEQUENCE HAVING RECURSIVE ENTRIES
    • Highly Influenced
    Certain matrices related to Fibonacci sequence having recursive entries
    • 2
    • Highly Influenced
    • PDF
    Triangular sequences, combinatorial recurrences and linear difference equations
    • Highly Influenced
    • PDF
    Statistics on wreath products and generalized binomial-stirling numbers
    • 18
    • PDF

    References

    SHOWING 1-10 OF 17 REFERENCES
    A characterization of inverse relations
    • 25
    Riordan arrays and combinatorial sums
    • 300
    • PDF
    Matrix Representation for Combinatorics
    • J. Kemeny
    • Computer Science, Mathematics
    • J. Comb. Theory, Ser. A
    • 1984
    • 5
    A new matrix inverse
    • 82
    • PDF
    Some new inverse series relations
    • 90
    Operator methods and Lagrange inversion: a unified approach to Lagrange formulas
    • 54
    • PDF
    Gaurav Bhatnagar
    • A characterization of inverse relations, Discrete Mathematics 193
    • 1998
    Concrete Mathematics
    • Concrete Mathematics
    • 1989