论文标题
约翰逊计划的张量功能的融合
Fusions of tensor powers of Johnson schemes
论文作者
论文摘要
本文是对（ARXIV：2203.03687）的后续措施，其中第一作者研究了笨拙协会方案的张量$ \ Mathcal {t} _M^d $之间的原始协会方案和hAmming Schemoce $ \ Mathcal {H}（H}（M，D）$。在该研究中自然出现的一个问题是，$ \ Mathcal {t} _m^d $的所有原始融合是否介于$ \ Mathcal {t} _ {M^e}^{d/e} $} $和$ \ MATHCAL {h}（H} $ e \ e）$中的一个$ e \ e \ e \ e \ e \ Mathcal {h} $ \ nathcal {h} $。如果$ m $足够大，则本说明正式回答了这个问题。我们类似地将约翰逊计划的$ d $ th张量功率的原始融合在$ \ binom {m} {k} $点上提供了$ m $，就$ k $和$ d $而言足够大。
This paper is a follow-up to (arXiv:2203.03687), in which the first author studied primitive association schemes lying between a tensor power $\mathcal{T}_m^d$ of the trivial association scheme and the Hamming scheme $\mathcal{H}(m,d)$. A question which arose naturally in that study was whether all primitive fusions of $\mathcal{T}_m^d$ lie between $\mathcal{T}_{m^e}^{d/e}$ and $\mathcal{H}(m^d, d/e)$ for some $e \mid d$. This note answers this question positively provided that $m$ is large enough. We similarly classify primitive fusions of the $d$th tensor power of a Johnson scheme on $\binom{m}{k}$ points provided $m$ is large enough in terms of $k$ and $d$.
