Interval Hypergraphs and Catalan Numbers
Résumé
An interval hypergraph is a hypergraph H=(V,E) such that there exists a linear order sigma (which is said to be compatible) on V such that, when V is sorted along sigma, every hyperedge is an interval of V. A interval cover of a set V is an interval hypergraph H=(V,E) such that $\bigcup_{e\in E}e = V$ and $\forall e,e'\in E, e\not\subset e'$.
In this note, we show that:
Nearly all interval hypergraphs have only two compatible orders.
The number of interval covers of {1,\ldots,n} is the Catalan number $C_{n}= \frac{1}{n+1}\binom{2n}{n}$.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...