|Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.5|
Abstract: The lattice of Dyck paths with the dominance partial order is studied. The notions of filling and degree of a Dyck path are introduced, studied and used for the evaluation of the Möbius function and its powers. The relation between the symmetric group endowed with the weak Bruhat order and the set of Dyck paths is studied.
(Concerned with sequences A000045 A000108 A006327 and A086581 .)
Received September 15 2005; revised version received April 18 2006. Published in Journal of Integer Sequences May 19 2006.