The poset of posets

Serge Bouc (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

Let X be a finite set. This paper describes some topological and combinatorial properties of the poset \Omega_X of order relations on X. In particular, the homotopy type of all the intervals in \Omega_X is precisely determined, and the Möbius function of \Omega_X is computed.

Mots clés: poset; order; Möbius function; homotopy type

Domaines: Topologie algébrique [math.AT]; Combinatoire [math.CO]; Théorie des groupes [math.GR]

Serge Bouc. The poset of posets. 2013. ⟨hal-00881858⟩