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Algebraic properties of crowns and fences. (English) Zbl 0695.08005

The authors study the clones of all order preserving operations for crowns and fences. Generating sets are presented and it is shown that these clones are finitely generated. Various related questions are also discussed.
Reviewer: A.Hatvany

MSC:

08A40 Operations and polynomials in algebraic structures, primal algebras
06A06 Partial orders, general
Full Text: DOI

References:

[1] K. A. Baker and A. F. Pixley (1975) Polynomial interpolation and the Chinese Remainder Theorem for algebraic systems. Math. Z. 143, 165-174. · doi:10.1007/BF01187059
[2] G. Birkhoff (1946). Sobre los grupos de automorfismos, Rev. Un. Mat. Argentina 11, 155-157.
[3] J. Demetrovics, L. Hannák, and L. Rónyai (1984) Near unanimity functions of partial orders, Proc. 14th Internat. Symp. Multiple Valued Logics, Manitoba, pp. 52-56.
[4] J. Demetrovics, L. Hannák, and L. Rónyai (1986) On algebraic properties of monotone clones, Order 3, 219-225. · Zbl 0613.08003 · doi:10.1007/BF00400285
[5] J. Demetrovics, L. Hannák, and L. Rónyai (1987) On monotone clones, MTA SZTAKI Tanulmányok, 202, 39-62.
[6] R. Frucht (1950) On the construction of partially ordered sets with a given group of automorphisms, Amer. J. Math. 72, 195-199. · Zbl 0035.01501 · doi:10.2307/2372146
[7] D. Duffus and I. Rival (1981) A structure theory of ordered sets, Discrete Math. 35, 53-118. · Zbl 0459.06002 · doi:10.1016/0012-365X(81)90201-6
[8] Z. Füredi and I. G. Rosenberg (1985) Orders admitting an isotone majority operation, Preprint CRM Université de Montréal. · Zbl 0894.06002
[9] J. Hashimoto (1948) On the product decomposition of partially ordered sets, Math. Japon. 1, 120-123. · Zbl 0041.37801
[10] S. V. Jablonskii (1958) Functional constructions in a k-valued logic (Russian), Trudy Mat. Inst. Steklov, 51, 5-142.
[11] D. Lau (1978) Bestimmung der Ordnung maximaler Klassen von Funktionen der k-wertigen Logik, Z. Math. Logik Grundlag. Math. 24, 79-96. · Zbl 0401.03008 · doi:10.1002/malq.19780240111
[12] P. Nevermann and I. Rival (1985) Holes in ordered sets, Graphic Combin. 1, 339-350. · Zbl 0606.06002 · doi:10.1007/BF02582962
[13] R. Pöschel and L. A. Kalu znin (1979) Funktionen und Relationenalgebren, Math. Monograph. Bd 15 VEB Deutscher Verlag der Wissenschaften, Berlin, Math. Reihe, Bd. 67, Birkhäuser Verlag Basel und Stuttgart.
[14] I. Rival (1976) A fixed point theorem for finite partially ordered sets, J. Combin. Theory A 21, 309-318. · Zbl 0357.06003 · doi:10.1016/0097-3165(76)90003-0
[15] I. G. Rosenberg (1985) Near unanimity orders, Preprint CRM Université de Montréal.
[16] Á. Szendrei (1986) Clones in Universal Algebra, Les Presses de l’Université de Montréal, 1986.
[17] G. Tardos (1986) A not finitely generated maximal clone of monotone operations, Order 3, 211-218. · Zbl 0614.08006 · doi:10.1007/BF00400284
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