A Note on Thin P-Polynomial and Dual-Thin Q-Polynomial Symmetric Association Schemes
Garth A. Dickie
and Paul M. Terwilliger
DOI: 10.1023/A:1008690026999
Abstract
Let Y denote a d-class symmetric association scheme, with d 
3. We show the following: If Y admits a P-polynomial structure with intersection numbers p ij h and Y is 1-thin with respect to at least one vertex, then p ll l =0 
p li i =0 1 
i - 1. If Y admits a Q-polynomial structure with Krein parameters q ij h , and Y is dual 1-thin with respect to at least one vertex, then q ll l = 0 q li i = 01 i d-1.
3. We show the following: If Y admits a P-polynomial structure with intersection numbers p ij h and Y is 1-thin with respect to at least one vertex, then p ll l =0 p li i =0 1 i - 1. If Y admits a Q-polynomial structure with Krein parameters q ij h , and Y is dual 1-thin with respect to at least one vertex, then q ll l = 0 q li i = 01 i d-1.Pages: 5–15
Keywords: association scheme; distance-regular graph; intersection number; Q-polynomial
Full Text: PDF
References
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2. P. Cameron, J. Goethals, and J. Seidel, “The Krein condition, spherical designs, Norton algebras, and permutation groups,” Indag. Math. 40 (1978), 196-206.
3. G. Dickie. “A note on Q-polynomial association schemes,” J. Alg. Combin. Submitted.
4. P. Terwilliger. “The subconstituent algebra of an association scheme. I,” J. Alg. Combin. 1(4) (1992), 363-388.
2. P. Cameron, J. Goethals, and J. Seidel, “The Krein condition, spherical designs, Norton algebras, and permutation groups,” Indag. Math. 40 (1978), 196-206.
3. G. Dickie. “A note on Q-polynomial association schemes,” J. Alg. Combin. Submitted.
4. P. Terwilliger. “The subconstituent algebra of an association scheme. I,” J. Alg. Combin. 1(4) (1992), 363-388.