AI 中文总结
针对所有块大小相同的t-设计，证明了舒阿纳尔关于有限非平凡简单图论t-平衡设计的猜想，且不要求设计简单，参数可由λ的显式多项式界定。
AI 中文摘要
完全图边集上的t-平衡设计若其块多重集在对称群对顶点的诱导作用下保持不变，则称为图论设计。舒阿纳尔猜想：对每个固定的指数λ，仅存在有限个非平凡的简单图论t-平衡设计满足t>1。我们针对t-设计证明了该猜想，t-设计是所有块大小相同的t-平衡设计。我们的定理不要求设计是简单的，且将设计的所有参数用λ的显式多项式界定。
英文摘要
A $t$-wise balanced design on the edge set of a complete graph is graphical if its block multiset is invariant under the induced action of the symmetric group on the vertices. Chouinard conjectured that, for each fixed index $λ$, there are only finitely many nontrivial simple graphical $t$-wise balanced designs with $t>1$. We prove the conjecture for $t$-designs, which are the $t$-wise balanced designs whose blocks all have the same size. Our theorem does not require simplicity, and we bound all parameters of the designs by explicit polynomials in $λ$.
Comments15 pages
