Anstee的两个定理的订正

本文的目的有二个,其一是给出反例说明Anstee的两个定理是欠妥的,其二是订正这二个定理。为方便起见,我们沿用[2]中的有关记号和定义。 设R和S分别为m维和n维非负整数向量,P=(P_(ij))_(m×n)为每列至多有一个1的(0,1)-矩阵。令_p(R,S)是一切以R为行和向量、S为列和向量且覆盖(cover)P的(0,1)-矩阵组成的集合。一个列向量a若是_p(R,S)中某个矩阵的第k列,则称a为_p(R,S)的

A Correction to Two Theorems Due to Anstee

In this paper we have constructed some counter examples, showing that Theorem 5.1 and Theorem 5.2 in [2] are incorrect. The fact is that formulas (5.2) and (5.4) in [2] are incorrect, and moreover, the invariant 1's and invariant 0's in U_p(R,S) are ignored. We have made a corretion to the two theorems, i. e. Theorem 5.1 and Theorem 5.2 in [2] are correct whenever k = n.