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Gale-Ryser Theorem

Let p and q be partitions of a positive integer, then there exists a (0,1)-matrix A such that c(A)=p, r(A)=q iff q is dominated by p^*.

See also

(0,1)-Matrix, Partition

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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 A(R,S)." Combinatorial Mathematics. Buffalo, NY: Math. Assoc. Amer., pp. 61-65, 1963.

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Gale-Ryser Theorem

Cite this as:

Weisstein, Eric W. "Gale-Ryser Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Gale-RyserTheorem.html

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