Bivariate P- and Q-polynomial structures of the association schemes based on attenuated spaces
The bivariate $P$- and $Q$-polynomial structures of association schemes based on attenuated spaces are examined using recurrence and difference relations of the bivariate polynomials which form the eigenvalues of the scheme. These bispectral properties are obtained from contiguity relations of univariate dual $q$-Hahn and affine $q$-Krawtchouk polynomials. The bispectral algebra associated to the bivariate polynomials is investigated, as well as the subconstituent algebra of the schemes. The properties of the schemes are compared to those of the non-binary Johnson schemes through a limit.
Authors
- Meri Zaimi (ORCID: https://orcid.org/0000-0001-7275-2007)
- Nicolas Crampé (ORCID: https://orcid.org/0000-0002-3754-4074)
- Pierre-Antoine Bernard (ORCID: https://orcid.org/0000-0002-6166-8528)
- Luc Vinet (ORCID: https://orcid.org/0000-0001-6211-7907)
- Xiaohong Zhang (ORCID: https://orcid.org/0000-0002-6732-2499)
Institutions
- Université de Tours (FR)
- Université d'Orléans (FR)
- Laboratoire d'Annecy de Physique Théorique (FR)
- Institut Denis Poisson (FR)
- Institut de Valorisation des Données
- Université de Montréal (CA)
Publication Details
- Journal
- Discrete Mathematics
- Published
- 2024-11-28
- DOI
- https://doi.org/10.1016/j.disc.2024.114332
- Citations
- 2
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 2.02
Funders
- Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada
- Centre National de la Recherche Scientifique
- Natural Sciences and Engineering Research Council of Canada