| The Intersection Problem for Kite-GDDs of Type $2^{u}$ |
| Received:November 10, 2020 Revised:May 20, 2021 |
| Key Words:
kite-GDD group divisible design intersection number
|
| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11601137) and the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region (Grant Nos.NJZY19231; NJZZ21052). |
|
| Hits: 516 |
| Download times: 462 |
| Abstract: |
| The intersection problem for kite-GDDs is the determination of all pairs $(T,s)$ such that there exists a pair of kite-GDDs $(X,{\cal H},{\cal B}_1)$ and $(X,{\cal H},{\cal B}_2)$ of the same type $T$ satisfying $|{\cal B}_1\cap {\cal B}_2|=s$. In this paper the intersection problem for a pair of kite-GDDs of type $2^u$ is investigated. Let $J(u)=\{s:$ $\exists$ a pair of kite-GDDs of type $2^u$ intersecting in $s$ blocks$\}$; $I(u)=\{0,1,\ldots,b_{u}-2,b_{u}\}$, 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 $J(3)= \{0,3\}$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2021.06.001 |
| View Full Text View/Add Comment |
|
|
|
