The intersection problem for kite-GDDs of type \(2^u\). (English) Zbl 1499.05070
Summary: The intersection problem for kite-GDDs is the determination of all pairs \((T, s)\) such that there exists a pair of kite-GDDs \((X, \mathcal{H}, \mathcal{B}_1)\) and \((X,\mathcal{H},\mathcal{B}_2)\) of the same type \(T\) satisfying \(|\mathcal{B}_1\cap\mathcal{B}_2| = s\). In this paper the intersection problem for a pair of kite-GDDs of type \(2^u\) is investigated. Let \(J(u)=\{s: \exists \text{ a pair of kite-GDDs of type } 2^u \text{ intersecting in } s \text{ blocks}\}\); \(I(u)=\{0, 1, \dots, b_u-2, b_u\}\), where \(b_u=u(u-1)/2\) is the number of blocks of a kite-GDD of type \(2^u\). We show that for any positive integer \(u\geq 4\), \(J(u)=I(u)\) and \(J(3)= \{0, 3\}\).
MSC:
| 05B05 | Combinatorial aspects of block designs |
| 05B30 | Other designs, configurations |
| 05C51 | Graph designs and isomorphic decomposition |
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