Geodesic
Parking functions of types A and B
The electronic journal of combinatorics, Tome 9 (2002)
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The lattice of noncrossing partitions can be embedded into the Cayley graph of the symmetric group. This allows us to rederive connections between noncrossing partitions and parking functions. We use an analogous embedding for type B non-crossing partitions in order to answer a question raised by R. Stanley on the edge labeling of the type B non-crossing partitions lattice.
DOI : 10.37236/1668
Classification : 06A07, 05A17, 20C30
Mots-clés : symmetric group, parking function, lattice of non-crossing partitions, refinement order, edge-labeling, maximal chains, Cayley graph 
@article{10_37236_1668,
     author = {P. Biane},
     title = {Parking functions of types {A} and {B}},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1668},
     zbl = {0999.06006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1668/}
}
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P. Biane. Parking functions of types A and B. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1668

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