D. Wang

collaborators

2 papers

math.CO2026

All parallel chip-firing games with $2∣ E ∣ - ∣ V ∣ < ∣ σ ∣ < 2∣ E ∣$ have period $2$

Daniel Wang, Nathan Lannan

In 2010, Levine found that the activity functions of parallel chip-firing games on the complete graph $K_{n}$ converge to a devil's staircase pattern: adding chips causes activity to…

math.CO2025

Periods and atomic firing sequences of parallel chip-firing games on directed graphs

David Ji, Michael Li, Daniel Wang

In 1992, Bitar and Goles introduced the parallel chip-firing game on undirected graphs. Two years later, Prisner extended the game to directed graphs. While the properties of paral…

All parallel chip-firing games with 2∣E∣−∣V∣<∣σ∣<2∣E∣ have period 2

Periods and atomic firing sequences of parallel chip-firing games on directed graphs

All parallel chip-firing games with $2∣ E ∣ - ∣ V ∣ < ∣ σ ∣ < 2∣ E ∣$ have period $2$