## Gale-Ryser Theorem

Let and be Partitions of a Positive Integer, then there exists a (0,1)-matrix such that , Iff is dominated by .

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.