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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Majorization on a partially ordered set


Author: F. K. Hwang
Journal: Proc. Amer. Math. Soc. 76 (1979), 199-203
MSC: Primary 06A10; Secondary 26B35
MathSciNet review: 537073
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Abstract: We extend the classical concept of set majorization to the case where the set is partially ordered. We give a useful property which characterizes majorization on a partially ordered set. Quite unexpectedly, the proof of this property relies on a theorem of Shapley on convex games. We also give a theorem which is parallel to the Schur-Ostrowski theorem in comparing two sets of parameters in a function.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0537073-0
PII: S 0002-9939(1979)0537073-0
Article copyright: © Copyright 1979 American Mathematical Society