Hahn Polynomials, Discrete Harmonics, and t-Designs
Hahn Polynomials, Discrete Harmonics, and t-Designs
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Hahn 多项式、离散谐波和 t 设计
DOI：
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发表时间：
1978
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通讯作者：
P. Delsarte
中科院分区：
文献类型：
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作者：
P. Delsarte
证明了某些Hahn多项式及其q-类似项在组合学中的作用类似于Gegenbauer多项式在实欧几里德几何中的作用。引入了正则格子纤维上调和函数的概念，并将Hahn多项式与定次调和空间联系起来。在此框架下，给出了t-设计的代数理论，并导出了设计基数的线性规划界。
It is shown that certain Hahn polynomials and their q-analogues play in combinatorics a similar role as Gegenbauer polynomials in real Euclidean geometry. The concept of harmonic function on a fiber of a regular lattice is introduced; then, Hahn polynomials are associated with harmonic spaces of fixed degrees. An algebraic theory of t-designs is presented in this framework, and a linear programming bound is derived for the cardinality of a design.