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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 10, Pages 607-616
http://dx.doi.org/10.1155/S0161171203206086

Extended blocker, deletion, and contraction maps on antichains

Data-Center Company, P.O. Box 5, Ekaterinburg RU-620034, Russia

Received 18 June 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Families of maps on the lattice of all antichains of a finite bounded poset that extend the blocker, deletion, and contraction maps on clutters are considered. Influence of the parameters of the maps is investigated. Order-theoretic extensions of some principal relations for the set-theoretic blocker, deletion, and contraction maps on clutters are presented.