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Spectra of Bipartite P- and Q-Polynomial Association Schemes

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Abstract.

 Let Y=(X,{R i }0≤i≤D) denote a symmetric association scheme with D≥3, and assume Y is not an ordinary cycle. Suppose Y is bipartite P-polynomial with respect to the given ordering A 0, A 1,…, A D of the associate matrices, and Q-polynomial with respect to the ordering E 0, E 1,…,E D of the primitive idempotents. Then the eigenvalues and dual eigenvalues satisfy exactly one of (i)–(iv).

(i)

(ii) D is even, and

(iii) θ* 00, and

(iv) θ* 00, D is odd, and

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Received: February 13, 1996 / Revised: October 16, 1996

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Caughman, J. Spectra of Bipartite P- and Q-Polynomial Association Schemes. Graphs Comb 14, 321–343 (1998). https://doi.org/10.1007/s003730050034

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  • DOI: https://doi.org/10.1007/s003730050034

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