Homomorphic Image Orders on Combinatorial Structures
- 102 Downloads
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.
KeywordsPartial order Homomorphism Combinatorial structure
Mathematics Subject Classifications (2010)Primary 06A06 Secondary 05C60, 06A07, 05C20, 05C05, 05A05
Unable to display preview. Download preview PDF.
- 2.Brignall, R.: A survey of simple permutations. Permutation patterns, pp. 41–65, London Math. Soc. Lecture Note Ser. 376. Cambridge University Press, Cambridge (2010)Google Scholar
- 6.Hell, P., Nešetřil, J.: Graphs and Homomorphisms. Oxford Lecture Series in Mathematics and Its Applications 28. Oxford University Press, Oxford (2004)Google Scholar