Gale-Ryser Theorem

Let and be partitions of a positive integer, then there exists a (0,1)-matrix such that , iff is dominated by .

Explore with Wolfram|Alpha

More things to try:

partitions
asymptotes (2x^3 + 4x^2 - 9)/(3 - x^2)
f'(t) = f(t)^2 + 1

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 Theorem

Cite this as:

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

Gale-Ryser Theorem

See also

Explore with Wolfram|Alpha

References

Referenced on Wolfram|Alpha

Cite this as:

Subject classifications