论文标题
关于某些原始$ Q $ - 多种物质的同构，而不是$ p $ - 多层协会方案
On the isomorphism of certain primitive $Q$-polynomial not $P$-polynomial association schemes
论文作者
论文摘要
2011年，Penttila和Williford建造了一个无限的新家族，由原始的$ Q $ - 多项式3级协会方案，不是源于距离常规图形，通过探索单一极性空间$ h（3，q^2）$，$ q $的几何形状，即使是符合符号的极性空间$ w（3，q^2）$，$ q $，均与符合性的极空$ W（3，Q $ w（3，Q 3，Q 3，3，Q）。 在与Penttila和Williford的私人沟通中，H。〜Tanaka指出，这些方案的参数与Hollmann和Hollmann和Xiang在2006年发现的3级方案相同，原因是考虑$ \ Mathrm {pgl}（pgl}（2，q^2）$，$ q $，$ q $，$ q $，$ q $偶，$ q $ co $ $ \ mathrm {pg}（2，q^2）$ extered在$ \ mathrm {pg}（2，q^4）$中。因此，出现了上述关联方案是否是同构的问题。在本文中，我们提供了积极的答案。与产品一样，我们得到了强烈规则图的同构。
In 2011, Penttila and Williford constructed an infinite new family of primitive $Q$-polynomial 3-class association schemes, not arising from distance regular graphs, by exploring the geometry of the lines of the unitary polar space $H(3,q^2)$, $q$ even, with respect to a symplectic polar space $W(3,q)$ embedded in it. In a private communication to Penttila and Williford, H.~Tanaka pointed out that these schemes have the same parameters as the 3-class schemes found by Hollmann and Xiang in 2006 by considering the action of $\mathrm{PGL}(2,q^2)$, $q$ even, on a non-degenerate conic of $\mathrm{PG}(2,q^2)$ extended in $\mathrm{PG}(2,q^4)$. Therefore, the question arises whether the above association schemes are isomorphic. In this paper we provide the positive answer. As by product, we get an isomorphism of strongly regular graphs.
