對偶集合系相關組合結構的一些研究

Abstract

一個(0,1)-矩陣可以對應一對互為對偶的集合系。若干組合結構，如2-設計、不完全平衡區組設計、對稱設計、擬對稱設計都是由內積在這個架構下來定義。若將內積改為布林和，則可在前述互為對偶的集合系上，考慮另一類的組合結構，這些結構可應用於提供具偵錯、改錯能力能的無序群試上，這個方法提供灘空間以及容許誤差的無序群試上的概念。

Each (0,1)-matrix is associated with a dual pair of set systems naturally. Some classical combinatorial structures including 2-designs, symmetric designs, quasi-symmetric designs are defined within this framework. In terms of union or Boolean sums, some conditions were posed over a dual pair of set systems, so that it provides a way for the notion of pooling spaces and the non-adaptive group testing with error-tolerance.