Extending partial permutation matrices
Author:
Charles C. Lindner
Journal:
Proc. Amer. Math. Soc. 24 (1970), 834
MSC:
Primary 05.24
DOI:
https://doi.org/10.1090/S0002-9939-1970-0255427-9
MathSciNet review:
0255427
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Abstract | References | Similar Articles | Additional Information
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.
- J. Marica and J. Schönheim, Incomplete diagonals of Latin squares, Canad. Math. Bull. 12 (1969), 235. MR 246786, DOI https://doi.org/10.4153/CMB-1969-030-5
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Keywords:
<!– MATH $n \times n$ –> <IMG WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$n \times n$"> arrays,
main diagonal,
permutation matrices,
<IMG WIDTH="56" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img15.gif" ALT="$(0,\;1)$"> matrix,
partial latin square
Article copyright:
© Copyright 1970
American Mathematical Society