Lucky Cars: Expected Values and Generating Functions

Abstract

We count lucky cars in parking functions of a given length, and provide elementary derivations for the generating functions, expected values and variances. We consider not only classical parking functions, but also problems with additional parking slots, and with cars of different sizes.

MSC:

• 05A15
• 60C05

Notes

1 The authors of [2] prefer the term “parking sequence,” which might be more appropriate, but we stick to “parking function” for the sake of consistency.

Additional information

Notes on contributors

Antonín Slavík

Antonín Slavík is associate professor at Charles University in Prague. His mathematical interests include differential and difference equations, integration theory, and history of mathematics.

Charles University, Faculty of Mathematics and Physics,

Sokolovská 83, 186 75 Praha 8, Czech Republic

[email protected]

Marie Vestenická

Marie Vestenická has recently earned a bachelor’s degree from Charles University in Prague. The present paper originated from her thesis dealing with parking problems.

Charles University, Faculty of Mathematics and Physics,

Sokolovská 83, 186 75 Praha 8, Czech Republic

[email protected]