13 papers
Parking Cascades: From the Simplest Sequence to Motzkin and Catalan
Ben Adenbaum, Néstor F. Díaz Morera, Jennifer Elder +3
We introduce -cascading parking functions, a parametrized variant of parking functions in which cars form bumping cascades of up to cars. Setting recovers cla…
Lehmer Parking Functions and Their Outcomes
Melissa Beerbower, Jennifer Elder, Pamela E. Harris +4
We introduce Lehmer parking functions and study their set of parking outcomes. Our main results establish that the number of outcomes of Lehmer parking functions of length is g…
Lucky Cars in Fubini Rankings and Unit Fubini Rankings
Camilo Barreto, Melissa Beerbower, Jennifer Elder +6
We study lucky cars in subsets of parking functions, called Fubini rankings and unit Fubini rankings. A Fubini ranking is a sequence of nonnegative integers that encodes a valid ra…
Inversions in parking functions
Kyle Celano, Jennifer Elder, Kimberly P. Hadaway +3
In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled…
Statistics on -interval parking functions
Kyle Celano, Jennifer Elder, Kimberly P. Hadaway +4
The displacement of a car with respect to a parking function is the number of spots it must drive past its preferred spot in order to park. An -interval parking function is o…
Enumerating Flat Fubini Rankings
Kenny Barrese, Jennifer Elder, Pamela E. Harris +1
Recall that the set of Fubini rankings on competitors consists of the -tuples that encode the possible rankings of competitors in a competition allowing ties. Moreover,…
Pullback parking functions
Jennifer Elder, Pamela E. Harris, Lybitina Koene +3
We introduce a generalization of parking functions in which cars are limited in their movement backwards and forwards by two nonnegative integer parameters and , respecti…
Boolean intervals in the weak Bruhat order of a finite Coxeter group
Ben Adenbaum, Jennifer Elder, Pamela E. Harris +1
Given a Coxeter group with Coxeter system , where is finite. We provide a complete characterization of Boolean intervals in the weak order of uniformly for all C…
On the Lucky and Displacement Statistics of Stirling Permutations
Laura Colmenarejo, Aleyah Dawkins, Jennifer Elder +5
Stirling permutations are parking functions, and we investigate two parking function statistics in the context of these objects: lucky cars and displacement. Among our results, we…
Cyclic sieving on permutations -- an analysis of maps and statistics in the FindStat database
Ashleigh Adams, Jennifer Elder, Nadia Lafrenière +3
We perform a systematic study of permutation statistics and bijective maps on permutations using SageMath to search the FindStat combinatorial statistics database to identify appar…
Unit interval parking functions and the -Fubini numbers
S. Alex Bradt, Jennifer Elder, Pamela E. Harris +5
We recall that unit interval parking functions of length are a subset of parking functions in which every car parks in its preference or in the spot after its preference, and F…
Interval and -interval Rational Parking Functions
Tomás Aguilar-Fraga, Jennifer Elder, Rebecca E. Garcia +12
Interval parking functions are a generalization of parking functions in which cars have an interval preference for their parking. We generalize this definition to parking functions…
Cost-sharing in Parking Games
Jennifer Elder, Pamela E. Harris, Jan Kretschmann +1
In this paper, we study the total displacement statistic of parking functions from the perspective of cooperative game theory. We introduce parking games, which are coalitional cos…