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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Extending partial permutation matrices


Author: Charles C. Lindner
Journal: Proc. Amer. Math. Soc. 24 (1970), 834
MSC: Primary 05.24
MathSciNet review: 0255427
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Abstract: Let $ {M_1},\;{M_2}, \cdots ,\;{M_s}$ be $ n \times n$ arrays such that in each $ {M_i}$, each cell is either empty or occupied by a $ 1$. It is shown that if $ {M_1} + {M_2} + \cdots + {M_s}$ contains only $ 1$'s, the totality of $ 1$'s is less than or equal to $ n - 1$, and the $ 1$'s are in different rows and columns, then the $ {M_i}$'s can be completed to permutation matrices $ M_1' , \cdots ,M_s'$ so that $ M_1' + \cdots + M_s'$ is a $ (0,\;1)$-matrix.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0255427-9
Keywords: $ n \times n$ arrays, main diagonal, permutation matrices, $ (0,\;1)$ matrix, partial latin square
Article copyright: © Copyright 1970 American Mathematical Society