A Colorful Way to Park: An Introduction to Exact $k$-Typed Parking Functions
Aalliyah Celestine, Jacob van der Leeuw, Lina Liu

TL;DR
This paper introduces exact $k$-typed parking functions, a new variant of classical parking functions, establishing their unique correspondence with parking configurations and exploring their relation to other combinatorial objects.
Contribution
It defines exact $k$-typed parking functions and proves their one-to-one correspondence with parking configurations, expanding the combinatorial understanding of parking functions.
Findings
Each exact $k$-typed parking function corresponds uniquely to a parking configuration.
The set of all exact $k$-TPFs leading to the same configuration forms a disjoint subset.
Parking permutations of an exact $k$-TPF relate to other combinatorial objects.
Abstract
Parking functions are tuples that describe the parking of cars on a street with parking spots. In this paper, we define exact -typed parking functions (-TPFs) to be a variant of classical parking functions. We then establish that every exact -TPF of length , corresponds to a unique parking configuration . We observe that the collection of all exact -TPFs which result in the same configuration form a disjoint subset of all exact -TPFs. Lastly, we conclude by showing how parking permutations of an exact -TPF can be related to other combinatorial objects.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Computational Geometry and Mesh Generation · Advanced Graph Theory Research
