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Two results on a partial ordering of finite sequences

Martin Klazar (1993)

Commentationes Mathematicae Universitatis Carolinae

In the first part of the paper we are concerned about finite sequences (over arbitrary symbols) u for which E x ( u , n ) = O ( n ) . The function E x ( u , n ) measures the maximum length of finite sequences over n symbols which contain no subsequence of the type u . It follows from the result of Hart and Sharir that the containment a b a b a ≺ u is a (minimal) obstacle to E x ( u , n ) = O ( n ) . We show by means of a construction due to Sharir and Wiernik that there is another obstacle to the linear growth. In the second part of the paper we investigate whether...

Un algorithme de partition d'un produit direct d'ordres totaux en un nombre minimum de chaînes

Emmanuel Pichon, Philippe Lenca, Fabrice Guillet, Jian Wei Wang (1994)

Mathématiques et Sciences Humaines

Cette étude s'inscrit dans un prolongement algorithmique d'un travail de Bruno Leclerc, publié dans cette revue, qui discute de la taille maximum d'une antichaîne dans un produit direct P d'ordres totaux. On y présente un algorithme de partitionnement de P en un nombre minimum de chaînes. Enfin, on décrit brièvement une application à l'extraction de connaissance.

Une opérade anticyclique sur les arbustes

Frédéric Chapoton (2010)

Annales mathématiques Blaise Pascal

We define new combinatorial objects, called shrubs, such that forests of rooted trees are shrubs. We then introduce a structure of operad on shrubs. We show that this operad is contained in the Zinbiel operad, by using the inclusion of Zinbiel in the operad of moulds. We also prove that this inclusion is compatible with the richer structure of anticyclic operad that exists on Zinbiel and on moulds.

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