Spencer Backman

collaborators

2 papers

math.CO2026

Quantized rational chip-firing

Spencer Backman, Nicholas A. Loehr, Gregory S. Warrington

This article introduces a quantized chip-firing model with close connections to the theory of rational lattice paths and rational parking functions. Given a graph with a sink and p…

math.CO2024

Skeletal generalizations of Dyck paths, parking functions, and chip-firing games

Spencer Backman, Cole Charbonneau, Nicholas A. Loehr +3

For $0 \leq k \leq n - 1$ , we introduce a family of $k$ -skeletal paths which are counted by the $n$ -th Catalan number for each $k$ , and specialize to Dyck paths when $k = n - 1$ . We simila…