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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Large minimal realizers of a partial order
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by Stephen B. Maurer and I. Rabinovitch PDF
Proc. Amer. Math. Soc. 66 (1977), 211-216 Request permission

Abstract:

The size of a minimum realizer of a partial order is called the dimension of that partial order. Here we initiate the study of minimal realizers which are not minimum. As an aid to the study of such realizers, we associate to each minimal realizer certain critical digraphs. We characterize all such critical digraphs for the antichain on n elements, and consequently deduce that for $n \geqslant 4$, the maximum size of a minimal realizer is $[{n^2}/4]$.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 66 (1977), 211-216
  • MSC: Primary 06A10
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0450144-0
  • MathSciNet review: 0450144