On the Homomorphism Order of Labeled Posets

Kwuida, Léonard; Lehtonen, Erkko

doi:10.1007/s11083-010-9169-x

Cited by 8 publications

(3 citation statements)

References 24 publications

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“…Somewhat surprisingly, this order has received very little attention in the literature. In comparison, the homomorphism order, corresponding to the existence of any homomorphism between two structures, is much-studied ( [5], [10]), as are various related concepts such as the core of a graph ( [3]). …”

Section: Introductionmentioning

confidence: 99%

Homomorphic Image Orders on Combinatorial Structures

Huczynska

Ruškuc

2014

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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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Section: Introductionmentioning

confidence: 99%

Homomorphic Image Orders on Combinatorial Structures

Huczynska

Ruškuc

2014

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“…The ordered set P G , which forms a bounded distributive lattice, is very complicated: every countable ordered set embeds into P G [16,32,20]. More generally, the homomorphism order has been studied for various categories of finite relational structures [25,24,10,23].…”

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confidence: 99%

The Homomorphism Lattice Induced by a Finite Algebra

Davey

Gray

Pitkethly

2017

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Each finite algebra A induces a lattice L A via the quasi-order → on the finite members of the variety generated by A, where B → C if there exists a homomorphism from B to C. In this paper, we introduce the question: 'Which lattices arise as the homomorphism lattice L A induced by a finite algebra A?' Our main result is that each finite distributive lattice arises as L Q , for some quasi-primal algebra Q. We also obtain representations of some other classes of lattices as homomorphism lattices, including all finite partition lattices, all finite subspace lattices and all lattices of the form L ⊕ 1, where L is an interval in the subgroup lattice of a finite group.

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“…[8,9,15,16]), and on universal partially ordered structures in general (see e.g. [10,4,6,12,13,7,11]).…”

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confidence: 99%