Since their introduction by Konheim and Weiss, parking functions have evolved
into objects of surprising combinatorial complexity for their simple definitions. First,
we introduce these structures, give a brief history of their development and give a
few basic theorems about their structure. Then we examine the internal structures of
parking functions, focusing on the distribution of descents and inversions in parking
functions. We develop a generalization to the Catalan numbers in order to count
subsets of the parking functions. Later, we introduce a generalization to parking
functions in the form of k-blocked parking functions, and examine their internal
structure. Finally, we expand on the extension to the Catalan numbers, exhibiting
examples to explore its internal structure. These results continue the exploration of
the deep structures of parking functions and their relationship to other combinatorial
objects.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-08-853 |
| Date | 14 January 2010 |
| Creators | Schumacher, Paul R. |
| Contributors | Yan, Catherine |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation |
| Format | application/pdf |
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