Matrices in Combinatorial Problems

  • Bolian Liu
  • Hong-Jian Lai
Part of the Network Theory and Applications book series (NETA, volume 3)

Abstract

Consider the difference equation (also called recurrence relation) with given boundary conditions
$$ {u_{n + k}} = {a_{}}{u_{n + k - 1}} + {a_2}{u_{n + k - 2}} + \ldots + {a_k}{u_n} + {b_n}$$
(4.1)
$${u_i} = {c_l},0 \leqslant l \leqslant k - 1$$
(4.2)
where the constants a 1, ...a k , c 0 , ...,c k−1 and the sequence 〈b n 〉 are given. A solution to this equation is a sequence 〈u n 〉 satisfying (4.1) and (4.2). If b n = 0, for all n, then the resulting equation is the corresponding homogeneous equation to (4.1).

Keywords

Gout 

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Bolian Liu
    • 1
  • Hong-Jian Lai
    • 2
  1. 1.Department of MathematicsSouth China Normal UniversityGuangzhouP.R. China
  2. 2.Department of MathematicsWest Virginia UniversityMorgantownUSA

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