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Summing Symbols in Mutual Recurrences

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Computing and Combinatorics (COCOON 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6842))

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Abstract

The problem of summing a set of mutual recurrence relations with constant coefficients is investigated. A method is presented for summing an order d system of the form \(A(n) = \sum_{i=1}^dM_iA(n-i) + G(n)\), where A,G : ℕ → K m and M 1,…,M d  ∈ M m (K) for some field K and natural number m. The procedure expresses the sum \(\sum_{i=0}^n{A(i)}\) in terms of A(n),…,A(n − d), initial conditions and sums of the inhomogeneous term G(n).

This work was supported in part by the National Science Foundation under a Research Experiences for Undergraduates (REU) grant, NSF Award No. 1004409.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara, CA, USA

    Berkeley R. Churchill

  2. Department of Computer Science and Statistics, University of Rhode Island, Kingston, RI, USA

    Edmund A. Lamagna

Authors
  1. Berkeley R. Churchill
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  2. Edmund A. Lamagna
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas-Pan American, 78539, Edinburg, TX, USA

    Bin Fu

  2. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

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© 2011 Springer-Verlag Berlin Heidelberg

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Churchill, B.R., Lamagna, E.A. (2011). Summing Symbols in Mutual Recurrences. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_46

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  • DOI: https://doi.org/10.1007/978-3-642-22685-4_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22684-7

  • Online ISBN: 978-3-642-22685-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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