Invariant sets for classes of matrices of zeros and ones

Authors:
Richard A. Brualdi and Jeffrey A. Ross

Journal:
Proc. Amer. Math. Soc. **80** (1980), 706-710

MSC:
Primary 05B20

DOI:
https://doi.org/10.1090/S0002-9939-1980-0587961-2

MathSciNet review:
587961

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Abstract: Let denote the class of all matrices of 0's and 1's with row sum vector *R* and column sum vector *S*. A set is said to be invariant if each matrix in contains the same number of 1's in the positions . We prove that if there are no invariant singletons, then an invariant set satisfies or .

**[1]**R. A. Brualdi and J. A. Ross,*On Ryser's maximum term rank formula*, Linear Algebra and Appl.**29**(1980), 33-38. MR**562747 (81e:15008)****[2]**D. Gale,*A theorem on flows in networks*, Pacific J. Math.**7**(1957), 1073-1082. MR**0091855 (19:1024a)****[3]**H. J. Ryser,*Combinatorial properties of matrices of zeros and ones*, Canad. J. Math.**9**(1957), 371-377. MR**0087622 (19:379d)****[4]**-,*Combinatorial mathematics*, The Carus Mathematical Monographs, No. 14, The Mathematical Association of America; distributed by Wiley, New York, 1963. MR**0150048 (27:51)**

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0587961-2

Article copyright:
© Copyright 1980
American Mathematical Society