A bivariate $Q$-polynomial structure for the non-binary Johnson scheme
Abstract
The notion of multivariate - and -polynomial association scheme has been introduced recently, generalizing the well-known univariate case. Numerous examples of such association schemes have already been exhibited. In particular, it has been demonstrated that the non-binary Johnson scheme is a bivariate -polynomial association scheme. We show here that it is also a bivariate -polynomial association scheme for some parameters. This provides, with the -polynomial structure, the bispectral property (i.e. the recurrence and difference relations) of a family of bivariate orthogonal polynomials made out of univariate Krawtchouk and dual Hahn polynomials. The algebra based on the bispectral operators is also studied together with the subconstituent algebra of this association scheme.
Cite
@article{arxiv.2306.01882,
title = {A bivariate $Q$-polynomial structure for the non-binary Johnson scheme},
author = {Nicolas Crampe and Luc Vinet and Meri Zaimi and Xiaohong Zhang},
journal= {arXiv preprint arXiv:2306.01882},
year = {2023}
}
Comments
20 pages. arXiv admin note: text overlap with arXiv:2212.10824