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Normalized Matching in Direct Products of Partial Orders
Author(s) -
Hsieh W N.,
Kleitman D. J.
Publication year - 1973
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1973523285
Subject(s) - mathematics , rank (graph theory) , regular polygon , matching (statistics) , product (mathematics) , order (exchange) , population , partial derivative , pure mathematics , combinatorics , mathematical analysis , statistics , geometry , demography , finance , sociology , economics
In this paper we investigate the question: When does the direct product of partial orders each satisfying the normalized matching condition also satisfy it? A proof of Harper's result that a sufficient condition for this is that factor partial orders have rank populations that are multiplicatively convex, is presented. A general necessary and sufficient condition is described, and conditions which occur when one factor is a chain are obtained. In particular we show that under these circumstances it is necessary that the product order have multiplicatively convex population rank.