, Volume 32, Issue 2, pp 205–226 | Cite as

Homomorphic Image Orders on Combinatorial Structures

  • Sophie Huczynska
  • Nik Ruškuc


Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a surjective homomorphism between two structures. We distinguish between strong and induced forms of the order and explore how they behave in the context of different common combinatorial structures. We focus on three aspects: antichains and partial well-order, the joint preimage property and the dual amalgamation property. The two latter properties are natural analogues of the well-known joint embedding property and amalgamation property, and are investigated here for the first time.


Partial order Homomorphism Combinatorial structure 

Mathematics Subject Classifications (2010)

Primary 06A06 Secondary 05C60, 06A07, 05C20, 05C05, 05A05 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of St AndrewsFifeUK

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