Geodesic
On the dominance partial ordering of Dyck paths
Journal of integer sequences, Tome 9 (2006) no. 2
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.
Classification : 06A07, 06D99
Keywords: Dyck paths, lattices, dominating sequences 
@article{JIS_2006__9_2_a3,
     author = {Sapounakis,  A. and Tasoulas,  I. and Tsikouras,  P.},
     title = {On the dominance partial ordering of {Dyck} paths},
     journal = {Journal of integer sequences},
     year = {2006},
     volume = {9},
     number = {2},
     zbl = {1104.05003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2006__9_2_a3/}
}
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Sapounakis,  A.; Tasoulas,  I.; Tsikouras,  P. On the dominance partial ordering of Dyck paths. Journal of integer sequences, Tome 9 (2006) no. 2. http://geodesic.mathdoc.fr/item/JIS_2006__9_2_a3/