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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

Span Tree Adjacency Matrix Complete Graph Regular Graph Combinatorial Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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