Algebraic properties of crowns and fences

Demetrovics, János; Rónyai, Lajos

doi:10.1007/bf00341639

Cited by 21 publications

(16 citation statements)

References 8 publications

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“…Proof (1) Crowns are shown to be Słupecki in [3] (for a more general result, including the case of truncated boolean lattices, see [2]).…”

Section: P Is Słupecki 2 If F : P S → P Is Not In the Component Of mentioning

confidence: 99%

Strongly Projective Graphs

Larose¹

2002

Can. j. math.

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Abstract. We introduce the notion of strongly projective graph, and characterise these graphs in terms of their neighbourhood poset. We describe certain exponential graphs associated to complete graphs and odd cycles. We extend and generalise a result of Greenwell and Lovász [6]: if a connected graph G does not admit a homomorphism to K, where K is an odd cycle or a complete graph on at least 3 vertices, then the graph G × K s admits, up to automorphisms of K, exactly s homomorphisms to K.

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“…Proof (1) Crowns are shown to be Słupecki in [3] (for a more general result, including the case of truncated boolean lattices, see [2]).…”

Section: P Is Słupecki 2 If F : P S → P Is Not In the Component Of mentioning

confidence: 99%

Strongly Projective Graphs

Larose¹

2002

Can. j. math.

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“…But in this case the algebra A ¼ ðA; F A Þ has no finite set F A of fundamental operations [16]. In [4] it was shown that for fences the variety V ð AÞ is congruence distributive and the algebra A can be represented by finitely many fundamental operations. If A is finite, there are only finitely many maximal subclones of Oð AÞ: Every proper subclone of Oð AÞ is contained in a maximal one.…”

Section: Introductionmentioning

confidence: 98%

On Constantive Simple and Order-Primal Algebras

Denecke

Radelecki

Ratanaprasert

2005

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A finite algebra A ¼ ðA; F A Þ is said to be order-primal if its clone of all term operations is the set of all operations defined on A which preserve a given partial order e on A. In this paper we study algebraic properties of order-primal algebras for connected ordered sets (A; e). Such order-primal algebras are constantive, simple and have no non-identical automorphisms. We show that in this case F A cannot have only unary fundamental operations or only one at least binary fundamental operation. We prove several properties of the varieties and the quasi-varieties generated by constantive and simple algebras and apply these properties to order-primal algebras. Further, we use the properties of order-primal algebras to formulate new primality criteria for finite algebras. (2000): 08B05, 06A11, 06A06. Mathematics Subject Classification

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“…It is an open question related to Tardos's result whether the clone of every locked crown is non-finitely generated. The positive answer to this question would be somewhat surprising at the first sight, since Demetrovics and Rónyai have proved in [3] that the clone of monotone operations of any crown is finitely generated. However, from results of the third author in [13] it follows that the clone of C is non-finitely generated if C is the four element crown.…”

Section: Introductionmentioning

confidence: 99%

“…In the proof of the characterization of critical relations of crowns, one of the main tools is a result of Demetrovics and Rónyai in [3] that states that every monotone surjective operation of a crown is essentially unary. As a consequence of our result, we also prove that SMP(C ), and hence RExt(C ), is solvable in polynomial time if C is a crown.…”

Section: Introductionmentioning

confidence: 99%