Homomorphism-Homogeneous Partially Ordered Sets |
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Authors: | Dragan Mašulović |
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Institution: | (1) Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia |
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Abstract: | A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism
of the structure. Recently, P. J. Cameron and J. Nešetřil introduced a relaxed version of homogeneity: we say that a structure
is homomorphism-homogeneous if every homomorphism between finite substructures of the structure extends to an endomorphism
of the structure. In this paper we characterize homomorphism-homogeneous partially ordered sets (where a homomorphism between
partially ordered sets A and B is a mapping f : A →B satisfying ). We show that there are five types of homomorphism-homogeneous partially ordered sets: partially ordered sets whose connected
components are chains; trees; dual trees; partially ordered sets which split into a tree and a dual tree; and X
5-dense locally bounded partially ordered sets.
Supported by the Ministry od Science and Environmental Protection of the Republic of Serbia, Grant No. 144017. |
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Keywords: | Partially ordered sets Homomorphism-homogeneous structures |
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