Homomorphic Image Orders on Combinatorial Structures

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 in...

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Bibliographic Details
Published inOrder (Dordrecht) Vol. 32; no. 2; pp. 205 - 226
Main Authors Huczynska, Sophie, Ruškuc, Nik
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.07.2015
Subjects
Algebra
Discrete Mathematics
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Homomorphism
Primary 06A06
Secondary 05C60, 06A07, 05C20, 05C05, 05A05
Combinatorial structure
Partial order
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Summary: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.
ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-014-9326-8