Lucky Cars and Lucky Spots in Parking Functions
Steve Butler, Kimberly Hadaway, Victoria Lenius, Preston Martens, and
Marshall Moats
Department of Mathematics
Iowa State University
Ames, IA 50011
USA
Abstract:
Parking functions correspond with preferences of n cars which enter
sequentially to park on a one-way street where (1) each car parks in
the first available spot greater than or equal to its preference and (2)
all cars successfully park. When a car parks in its preferred spot then
the corresponding car and corresponding spot are deemed "lucky". This
paper looks briefly at lucky cars which have previously been studied and
in simple cases can be understood by a generalization of a result due to
Pollak. We also consider lucky spots where the situation is more complex
and not previously studied. Probabilities and asymptotics for lucky spots
are given for the first few spots on the one-way street. We close with
an exploration of the special cases when cars enter the one-way street in
either weakly-increasing or weakly-decreasing order of their preferences.
Full version: pdf,
dvi,
ps,
latex
(Concerned with sequences
A001263
A002538
A067323
A298592
A298594
A372842
A372843
A372844
A372845
A374533
A374756
A375616.)
Received August 23 2024; revised versions received September 22 2025; October 10 2025;
December 19 2025.
Published in Journal of Integer Sequences,
December 20 2025.
Return to
Journal of Integer Sequences home page