Geodesic
A three-regime theorem for flow-firing
The electronic journal of combinatorics, Tome 32 (2025) no. 2
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Graphical chip-firing is a discrete dynamical system where chips are placed on the vertices of a graph and exchanged via simple firing moves. Recent work has sought to generalize chip-firing on graphs to higher dimensions, wherein graphs are replaced by cellular complexes and chip firing becomes flow-rerouting along the faces of the complex. Given such a system, it is natural to ask (1) whether this firing process terminates and (2) if it terminates uniquely (i.e. is confluent). In the graphical case, these questions were definitively answered by Bjorner-Lovasz-Shor, who developed three regimes which completely determine if a given system will terminate. Building on the work of Duval-Klivans-Martin and Felzenszwalb-Klivans, we answer these questions in a context called flow-firing, where the cellular complexes are 2-dimensional.
DOI : 10.37236/12841
Classification : 05C57, 91A43, 05C85
Mots-clés : chip-firing on graphs, flow-firing

Sarah Brauner    ; Galen Dorpalen-Barry    ; Selvi Kara  1   ; Caroline Klivans    ; Lisa Schneider  

1 Bryn Mawr College 
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     title = {A three-regime theorem for flow-firing},
     journal = {The electronic journal of combinatorics},
     year = {2025},
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Sarah  Brauner; Galen  Dorpalen-Barry; Selvi Kara; Caroline Klivans; Lisa  Schneider . A three-regime theorem for flow-firing. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/12841

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