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The pseudo-cosine sequences of a distance-regular graph

✍ Scribed by Arlene A. Pascasio; Paul Terwilliger

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 335 KB
Volume: 419
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.05.017

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✦ Synopsis

Let denote a distance-regular graph with diameter D 3, valency k, and intersection numbers a i , b i , c i . By a pseudo-cosine sequence of we mean a sequence of real numbers σ 0 , σ 1 , . . . , σ D such that σ 0 = 1 and c i σ i-1 + a i σ i + b i σ i+1 = kσ 1 σ i for 0 i D -1. Let σ 0 , σ 1 , . . . , σ D and ρ 0 , ρ 1 , . . . , ρ D denote pseudo-cosine sequences of . We say this pair of sequences is tight whenever σ 0 ρ 0 , σ 1 ρ 1 , . . . , σ D ρ D is a pseudo-cosine sequence of . In this paper, we determine all the tight pairs of pseudo-cosine sequences of .

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