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I want to do a project on "Parking Functions" but searching it on google gives all published papers on the topic. Moreover there is no page on Wikipedia or Wolfram about this topic!!

Can anyone refer to or give a link to an introductory article or note on the "Parking Functions"

A parking function is a function $f: \{1, \ldots n\} \rightarrow \{1, \ldots n\}$ which has the property that the list $(f(1), f(2), \ldots f(n))$ can be rearranged in some order $(a_{1}, a_{2}, \ldots a_{n})$ so that $a_{i} \leq i$ for each $i$.

Thank You!!

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1 Answer

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Dominique Foata & John Riordan, ‘Mappings of Acyclic and Parking Functions’, Aequationes mathematicae $\mathbf{10}$ ($1974$), $10$-$22$, isn’t bad. You might also look at John Riordan, ‘Ballots and trees’, Journal of Combinatorial Theory $\mathbf{6}$ ($1969$), $408$-$411$. And although it has quite a bit of other (related) material, Julian D. Gilbey & Louis H. Kalikow, ‘Parking functions, valet functions and priority queues’, Discrete Mathematics $\mathbf{197\text{-}198}$ ($1999$), $351$-$373$, offers a different view of parking functions that is quite helpful in thinking about them; an edited version is also available as the second part of Gilbey’s PhD thesis [PDF].

These are some of the papers that I looked at when one of my masters students did a project on parking functions some years ago.

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