### Abstract

For a v-set V, let A be a collection of r × c arrays with elements in V. A pair (V, A) is called an r × c grid-block packing if every two distinct points i and j in V occur together at most once in the same row or in the same column of arrays in A. And an r × c grid-block packing (V, A) is said to be resolvable if the collection of arrays A can be partitioned into sub-classes R_{1}, R_{2}, ..., R_{t} such that every point of V is contained in precisely one array of each class. These packings have originated from the use of DNA library screening. In this paper, we give some constructions of resolvable r × c grid-block packings and give a brief survey of their application to DNA library screening.

Original language | English |
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Pages (from-to) | 713-737 |

Number of pages | 25 |

Journal | Taiwanese Journal of Mathematics |

Volume | 8 |

Issue number | 4 |

DOIs | |

State | Published - 1 Jan 2004 |

### Keywords

- DNA library screening
- Grid-block design
- Grid-block packing
- Lattice square design

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## Cite this

*Taiwanese Journal of Mathematics*,

*8*(4), 713-737. https://doi.org/10.11650/twjm/1500407714