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no. 2
Bivariate P-polynomial association schemes
Bernard, Pierre-Antoine1; Crampé, Nicolas2; Poulain d’Andecy, Loïc3; Vinet, Luc1, 4; Zaimi, Meri1
1 Centre de Recherches Mathématiques Université de Montréal P.O. Box 6128 Centre-ville Station Montréal (Québec) H3C 3J7 Canada
2 Institut Denis-Poisson CNRS/UMR 7013 - Université de Tours - Université d’Orléans Parc de Grandmont 37200 Tours France
3 Laboratoire de mathématiques de Reims UMR 9008 Université de Reims Champagne-Ardenne Moulin de la Housse BP 1039 51100 Reims France
4 IVADO Montréal (Québec) H2S 3H1 Canada
Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 361-382.

Bivariate P-polynomial association scheme of type (α,β) are defined as a generalization of the P-polynomial association schemes. This generalization is shown to be equivalent to a set of conditions on the intersection parameters. A number of known higher rank association schemes are seen to belong to this broad class. Bivariate Q-polynomial association schemes are similarly defined.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.344
Classification: 05E30, 20C15
Keywords: association scheme, bivariate polynomials, metric

Bernard, Pierre-Antoine 1; Crampé, Nicolas 2; Poulain d’Andecy, Loïc 3; Vinet, Luc 1, 4; Zaimi, Meri 1

1 Centre de Recherches Mathématiques Université de Montréal P.O. Box 6128 Centre-ville Station Montréal (Québec) H3C 3J7 Canada
2 Institut Denis-Poisson CNRS/UMR 7013 - Université de Tours - Université d’Orléans Parc de Grandmont 37200 Tours France
3 Laboratoire de mathématiques de Reims UMR 9008 Université de Reims Champagne-Ardenne Moulin de la Housse BP 1039 51100 Reims France
4 IVADO Montréal (Québec) H2S 3H1 Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Bernard, Pierre-Antoine; Crampé, Nicolas; Poulain d’Andecy, Loïc; Vinet, Luc; Zaimi, Meri. Bivariate $P$-polynomial association schemes. Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 361-382. doi : 10.5802/alco.344. https://alco.centre-mersenne.org/articles/10.5802/alco.344/

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