• Citer

Counting biorders

par Christophe, Jean ;Doignon, Jean-Paul ;Fiorini, Samuel
Référence Journal of integer sequences, 6
Publication Publié, 2003

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

Biorders were introduced first as Guttman scales and then as Ferrers relations. They are now well recognized in combinatorics and its applications. However, it seems that no procedure besides plain enumeration was made available for obtaining the number of biorders from an m-element set to an n-element set. We establish first a double-recurrence formula for computing this number, and then two explicit formulas involving Stirling numbers of the second kind. Our methods do not seem to extend to other, similar structures. For instance, interval orders on a finite set are exactly the irreflexive biorders on that set. To our knowledge, no direct formula is available for deriving their number.