Geodesic
A decomposition of parking functions by undesired spaces
Melody Bruce1 ; Michael Dougherty2 ; Max Hlavacek3 ; Ryo Kudo4 ; Ian Nicolas5
1Western Carolina University
2University of California, Santa Barbara
3Harvey Mudd College
4University of California, Los Angeles
5Pacific University
The electronic journal of combinatorics, Tome 23 (2016) no. 3
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There is a well-known bijection between parking functions of a fixed length and maximal chains of the noncrossing partition lattice which we can use to associate to each set of parking functions a poset whose Hasse diagram is the union of the corresponding maximal chains. We introduce a decomposition of parking functions based on the largest number omitted and prove several theorems about the corresponding posets. In particular, they share properties with the noncrossing partition lattice such as local self-duality, a nice characterization of intervals, a readily computable Möbius function, and a symmetric chain decomposition. We also explore connections with order complexes, labeled Dyck paths, and rooted forests.
DOI : 10.37236/5940
Classification : 05A18, 06A07
Mots-clés : parking functions, noncrossing partitions

Melody Bruce  1   ; Michael Dougherty  2   ; Max Hlavacek  3   ; Ryo Kudo  4   ; Ian Nicolas  5

1 Western Carolina University
2 University of California, Santa Barbara
3 Harvey Mudd College
4 University of California, Los Angeles
5 Pacific University 
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     year = {2016},
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     number = {3},
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Melody Bruce; Michael Dougherty; Max Hlavacek; Ryo Kudo; Ian Nicolas. A decomposition of parking functions by undesired spaces. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/5940

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