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Endomorphisms of Partially Ordered Sets

  • DWIGHT DUFFUS (a1), TOMASZ ŁUCZAK (a1), VOJTĚCH RÖDL (a1) and ANDRZEJ RUCIŃSKI (a1)
    • Published online: 01 March 1998
Abstract

It is shown that every partially ordered set with n elements admits an endomorphism with an image of a size at least n1/7 but smaller than n. We also prove that there exists a partially ordered set with n elements such that each of its non-trivial endomorphisms has an image of size O((n log n)1/3).

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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