Let 
and 
be partitions of a positive
integer, then there exists a (0,1)-matrix 
such that 
, 
iff 
is dominated by 
.
Gale-Ryser Theorem
See also
(0,1)-Matrix, PartitionExplore with Wolfram|Alpha
References
Brualdi, R. and Ryser, H. J. §6.2.4 in Combinatorial Matrix Theory. New York: Cambridge University Press, 1991.Krause, M. "A Simple Proof of the Gale-Ryser Theorem." Amer. Math. Monthly 103, 335-337, 1996.Robinson, G. §1.4 in Representation Theory of the Symmetric Group. Toronto, Canada: University of Toronto Press, 1961.Ryser, H. J. "The Class
." Combinatorial
Mathematics. Buffalo, NY: Math. Assoc. Amer., pp. 61-65, 1963.Referenced on Wolfram|Alpha
Gale-Ryser TheoremCite this as:
Weisstein, Eric W. "Gale-Ryser Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Gale-RyserTheorem.html