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Posets, near unanimity functions and zigzags

Published online by Cambridge University Press:  17 April 2009

László Zádori
László Zádori
Affiliation:
Jóssef Attila Tudom-anyegyetem Bolyai Intéset Aradi vértanúk tere 1 H-6720 Szeged, Hungary
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Abstract

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With every poset we associate a class of coloured posets called zigzags. By means of zigzags we show that, if we delete a convex set from a finite lattice ordered set then the resulting poset has the strong selection property. We give the complete list of finite bounded irreducible posets admitting an n-ary near unanimity function, provided n ≤ 6. We present some examples and classes of posets with full descriptions of their zigzags.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 1 , February 1993 , pp. 79 - 93
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Davey, B. A., ‘Monotone clones and congruence modularity’, Order 6 (1990), 389–400.Google Scholar
[2]Davey, B. A., Quackenbush, R. W. and Schweigert, D., ‘Monotone clones and the varieties they determine’, Order 7 (1990), 145–167.Google Scholar
[3]Demetrovics, J., Hannák, L. and Rónyai, L., ‘Near unanimity functions of partial orders’, in Proc. 14 (ISMVL, Manitoba, 1984), pp. 52–56.Google Scholar
[4]Duffus, D. and Rival, I., ‘A structure theory for ordered sets’, Discrete Math. 35 (1981), 53 –118.Google Scholar
[5]McKenzie, R., ‘Algebraic properties of monotone clones: residual smallness and congruence distributivity’, Bull. Austral. Math. Soc. 41 (1990), 283–300.Google Scholar
[6]Nevermann, P. and Rival, I., ‘Holes in ordered sets’, Graphs Combin. 1 (1985), 339–350.Google Scholar
[7]Nevermann, P. and Wille, R., ‘The strong selection property and ordered sets of finite length’, Algebra. Universalis 18 (1984), 18–28.Google Scholar
[8]Quackenbush, R., Rival, I. and Rosenberg, I.G., ‘Clones, order varieties, near unanimity functions and holes’, Order 7 (1990), 239–248.Google Scholar
[9]Tardos, G., ‘A maximal clone of monotone operations which is not finitely generated’, Order 3 (1986), 211–218.Google Scholar
[10]Zadori, L., ‘Order varieties generated by finite posets’, Order 8 (1992), 341–348.Google Scholar
[11]Zadori, L., ‘Monotone Jónsson operations and near unanimity functions’, (submitted).Google Scholar