Traces of Matrices of Zeros and Ones
1960 ◽
Vol 12
◽
pp. 463-476
◽
Keyword(s):
This paper continues the study appearing in (9) and (10) of the combinatorial properties of a matrix A of m rows and n columns, all of whose entries are 0's and l's. Let the sum of row i of A be denoted by ri and let the sum of column j of A be denoted by Sj. We call R = (r1, … , rm) the row sum vector and S = (s1 . . , sn) the column sum vector of A. The vectors R and S determine a class1.1consisting of all (0, 1)-matrices of m rows and n columns, with row sum vector R and column sum vector S. The majorization concept yields simple necessary and sufficient conditions on R and S in order that the class 21 be non-empty (4; 9). Generalizations of this result and a critical survey of a wide variety of related problems are available in (6).
1981 ◽
Vol 91
(1-2)
◽
pp. 135-145
1980 ◽
Vol 32
(1)
◽
pp. 1-20
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1967 ◽
Vol 19
◽
pp. 757-763
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1975 ◽
Vol 18
(1)
◽
pp. 155-156
◽
1989 ◽
Vol 113
(1-2)
◽
pp. 159-180
◽
1976 ◽
Vol 76
(1)
◽
pp. 43-53
◽
1994 ◽
Vol 49
(1)
◽
pp. 69-79
◽
1980 ◽
Vol 21
(3)
◽
pp. 321-328
1988 ◽
Vol 8
(3)
◽
pp. 351-364
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