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Parking functions are a well-studied area of combinatorics that have connections to Cayley’s tree formula, Catalan numbers, Dyck paths, and much more. We connect parking functions to another classic car-related puzzle called the gas stations puzzle. Looking at it through this lens, we give two new proofs of results in this area that are natural extensions of the original connection.
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Tyler Seacrest (2025) studied this question.
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