تقرير
A bivariate $Q$-polynomial structure for the non-binary Johnson scheme
| العنوان: | A bivariate $Q$-polynomial structure for the non-binary Johnson scheme |
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| المؤلفون: | Crampe, Nicolas, Vinet, Luc, Zaimi, Meri, Zhang, Xiaohong |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | The notion of multivariate $P$- and $Q$-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 $P$-polynomial association scheme. We show here that it is also a bivariate $Q$-polynomial association scheme for some parameters. This provides, with the $P$-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. Comment: 20 pages. arXiv admin note: text overlap with arXiv:2212.10824 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2306.01882 |
| رقم الأكسشن: | edsarx.2306.01882 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |