Gale-Ryser Theorem

Let and be Partitions of a Positive Integer, then there existsa (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.

• Stieltjes Integral
• Stieltjes' Theorem
• Stieltjes-Wigert Polynomial
• Stirling Cycle Number
• Stirling Number of the First Kind
• Stirling Number of the Second Kind
• Stirling's Approximation
• Stirling Set Number
• Stirling's Finite Difference Formula
• Stirling's Formula
• Stirling's Series
• Stirrup Curve
• Stochastic
• Stochastic Calculus of Variations
• Stochastic Group
• Stochastic Matrix
• Stochastic Process
• Stochastic Resonance
• Stokes Phenomenon
• Stokes' Theorem
• Stolarsky Array
• Stolarsky-Harborth Constant
• Stolarsky's Inequality
• Stomachion
• Stone Space