Garrett Nelson

activity

20232025

collaborators

3 papers

math.CO2025

Rational parking functions and $(m, n)$ -invariant sets

Garrett Nelson

An $(m, n)$ -parking function can be characterized as function $f : [n] \to [m]$ such that the partition obtained by reordering the values of $f$ fits inside a right triangle with leg…

math.CO2024

Combinatorics of generalized parking-function polytopes

Margaret M. Bayer, Steffen Borgwardt, Teressa Chambers +8

For $b = (b_{1}, \dots, b_{n}) \in Z_{> 0}^{n}$ , a $b$ -parking function is defined to be a sequence $(β_{1}, \dots, β_{n})$ of positive integers whose nondecreasing rearra…

math.CO2023

Sampling planar tanglegrams and pairs of disjoint triangulations

Alexander E. Black, Kevin Liu, Alex Mcdonough +4

A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that th…

Rational parking functions and (m,n)-invariant sets

Combinatorics of generalized parking-function polytopes

Sampling planar tanglegrams and pairs of disjoint triangulations

Rational parking functions and $(m, n)$ -invariant sets