Displaying similar documents to “Image partition regularity over the integers, rationals and reals.”

Ranks of permutative matrices

Xiaonan Hu, Charles R. Johnson, Caroline E. Davis, Yimeng Zhang (2016)

Special Matrices

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A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.

Matrix compositions.

Munarini, Emanuele, Poneti, Maddalena, Rinaldi, Simone (2009)

Journal of Integer Sequences [electronic only]

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The difference matrices of the classes of a Sharma-Kaushik partition

Bhu Dev Sharma, Norris Sookoo (2004)

Archivum Mathematicum

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Sharma-Kaushik partitions have been used to define distances between vectors with n -coordinates. In this paper, “difference matrices” for the partitioning classes have been introduced and investigated. It has been shown that the difference matrices are circulant and that the entries of a product of matrices is an extended intersection number of a distance scheme. The sum of the entries of each row or columns of the product matrix has been obtained. The algebra of matrices generated by...