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CONCERNING PARTITION REGULAR MATRICES

机译:关于分区定期矩阵

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A finite or infinite matrix A with entries from Q is image partition regular provided that whenever N is finitely colored, there must be some ~x with entries from N such that all entries of A~x are in some color class. In 2003, Hindman, Leader and Strauss studied centrally image partition regular matrices and extended many results of finite image partition regular matrices to infinite image partition regular matrices. It was shown that centrally image partition regular matrices are closed under diagonal sums. In the present paper, we show that the diagonal sum of two matrices, one of which comes from the class of all Milliken-Taylor matrices and the other from a suitable subclass of the class of all centrally image partition regular matrices, is also image partition regular. This will produce more image partition regular matrices. We also study the multiple structures within one cell of a finite partition of N.
机译:具有来自Q条目的有限或无限矩阵A是图像分区常规,只要n为有限的彩色,就必须有一些〜x与n的条目,使得a〜x的所有条目都在某些颜色类中。 2003年,Hindman,Leader和Strauss研究了中心图像分区定期矩阵,并将有限图像分区定期矩阵的许多结果扩展到无限的图像分区常规矩阵。结果表明,中心图像分区常规矩阵在对角线下闭合。在本文中,我们表明,两个矩阵的对角线总和,其中一个来自所有Milliken-Taylor矩阵的类,另一个来自所有中央图像分区的类别的适当子类,也是图像分区常规的。这将产生更多的图像分区常规矩阵。我们还研究了N的一个单元格内的多个结构。

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