Spectra of Bipartite P- and Q-Polynomial Association Schemes |
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| Authors: | John S Caughman |
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| Institution: | (1) Department of Mathematics, University of Wisconsin, 480 Lincoln Dr., Madison, WI 53706, USA. e-mail: caughman@math.wisc.edu, US |
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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*
0>θ0, and
(iv) θ*
0>θ0, D is odd, and
Received: February 13, 1996 / Revised: October 16, 1996 |
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| Keywords: | |
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