Bachir Sadi - Suite d’ensembles partiellement ordonnés

arima:1846 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, November 26, 2006, Volume 4, 2006 - https://doi.org/10.46298/arima.1846
Suite d’ensembles partiellement ordonnés

Authors: Bachir Sadi 1

  • 1 Département de Mathématiques [Tizi Ouzou]

This work is to study an order D(P) on maximal antichains of a given order. D(P) is an order included in the order which defines the Lattice of maximal antichains AM(P), introduced by R.P. Dilworth, in 1960. In [3], T.Y. Kong and P. Ribenboim have proved that there exists an integer i such that Di(P) is a chain, where Di(P)=D(D(…D(P))), i times. We find the smallest i, noted cdev(P) such that Di(P) is a chain for some particular classes of orders and we approximate this parameter in the general case of order.

https://doi.org/10.46298/arima.1846
Source: HAL:hal-01262047v1
Volume: Volume 4, 2006
Published on: November 26, 2006
Submitted on: May 1, 2006
Keywords: Maximal antichain, order, partial order,Antichaîne maximale,ordre,ordre partiel,[INFO] Computer Science [cs],[MATH] Mathematics [math]

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