Jan Kretschmann

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4 papers · 1 filter

math.CO2023

On some discrete statistics of parking functions

Ari Cruz, Pamela E. Harris, Kimberly J. Harry +5

Recall that $α = (a_{1}, a_{2}, \dots, a_{n}) \in [n]^{n}$ is a parking function if its nondecreasing rearrangement $β = (b_{1}, b_{2}, \dots, b_{n})$ satisfies $b_{i} \leq i$ for all $1 \leq i \leq n$ . In thi…

math.CO2023

The structure and normalized volume of Monge polytopes

William Q. Erickson, Jan Kretschmann

A matrix $C$ has the Monge property if $c_{ij} + c_{I J} \leq c_{I j} + c_{i J}$ for all $i < I$ and $j < J$ . Monge matrices play an important role in combinatorial optimization; for…

math.CO2023

Interval and $ℓ$ -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…

math.CO2023

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…

On some discrete statistics of parking functions

The structure and normalized volume of Monge polytopes

Interval and ℓ-interval Rational Parking Functions

Cost-sharing in Parking Games

Interval and $ℓ$ -interval Rational Parking Functions