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Homomorphic Image Orders on Combinatorial Structures

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of St Andrews, Fife, KY16 9SS, UK

    Sophie Huczynska & Nik Ruškuc

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  1. Sophie Huczynska
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  2. Nik Ruškuc
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Correspondence to Sophie Huczynska.

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Huczynska, S., Ruškuc, N. Homomorphic Image Orders on Combinatorial Structures. Order 32, 205–226 (2015). https://doi.org/10.1007/s11083-014-9326-8

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  • DOI: https://doi.org/10.1007/s11083-014-9326-8

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