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Endomorphisms of Partially Ordered Sets

Published online by Cambridge University Press:  01 March 1998

DWIGHT DUFFUS ,
TOMASZ ŁUCZAK ,
VOJTĚCH RÖDL  and
ANDRZEJ RUCIŃSKI
DWIGHT DUFFUS
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA
TOMASZ ŁUCZAK
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA
VOJTĚCH RÖDL
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA
ANDRZEJ RUCIŃSKI
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA
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Abstract

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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).

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 1 , March 1998 , pp. 33 - 46
Copyright
1998 Cambridge University Press