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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Article copyright: © Copyright 1979 American Mathematical Society