基于衰减空间的结合方案的二元 $P$- 和 $Q$-多项式结构
Bivariate $P$- and $Q$-polynomial structures of the association schemes based on attenuated spaces
AI总结：
本文研究基于衰减空间的结合方案的二元 $P$/ $Q$-多项式结构，借助对偶 $q$-Hahn 与仿射 $q$-Krawtchouk 多项式的邻接关系揭示其双谱代数和子成分代数，并与非二元 Johnson 方案比较。
摘要：
本文利用构成该方案特征值的二元多项式的递推关系与差分关系，考察了基于衰减空间的结合方案的二元 $P$- 和 $Q$-多项式结构。这些双谱性质由一元对偶 $q$-Hahn 多项式与仿射 $q$-Krawtchouk 多项式的邻接关系得到。文中研究了与这些二元多项式相关的双谱代数，以及这些方案的子成分代数，并通过一个极限将这些方案的性质与非二元 Johnson 方案的性质进行了比较。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
