chipfiring: A Python Package for Efficient Mathematical Analysis of Chip-Firing Games on Multigraphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913974054813696 |
|---|---|
| author | Mavani, Dhyey Dharmendrakumar Ji, Tairan Pflueger, Nathan |
| author_facet | Mavani, Dhyey Dharmendrakumar Ji, Tairan Pflueger, Nathan |
| contents | This paper presents `chipfiring`, a comprehensive Python package for the mathematical analysis of chip-firing games on finite graphs. The package provides a robust toolkit for defining graphs and chip configurations (divisors), performing chip-firing operations, and analyzing fundamental properties such as winnability, linear equivalence, and divisor rank. We detail the core components of the library, including its object-oriented graph and divisor implementations, integrated Laplacian matrix computations, and an efficient implementation of Dhar's algorithm for determining the solvability of the dollar game. The `chipfiring` package is designed for researchers and students in graph theory, combinatorics, and algebraic geometry, providing essential algorithms and data structures for exploring these rich mathematical models. We describe the library's architecture, illustrate its usage with comprehensive examples, and highlight its specialized contributions compared to general-purpose graph libraries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | chipfiring: A Python Package for Efficient Mathematical Analysis of Chip-Firing Games on Multigraphs Mavani, Dhyey Dharmendrakumar Ji, Tairan Pflueger, Nathan Combinatorics Computational Geometry Mathematical Software Algebraic Geometry This paper presents `chipfiring`, a comprehensive Python package for the mathematical analysis of chip-firing games on finite graphs. The package provides a robust toolkit for defining graphs and chip configurations (divisors), performing chip-firing operations, and analyzing fundamental properties such as winnability, linear equivalence, and divisor rank. We detail the core components of the library, including its object-oriented graph and divisor implementations, integrated Laplacian matrix computations, and an efficient implementation of Dhar's algorithm for determining the solvability of the dollar game. The `chipfiring` package is designed for researchers and students in graph theory, combinatorics, and algebraic geometry, providing essential algorithms and data structures for exploring these rich mathematical models. We describe the library's architecture, illustrate its usage with comprehensive examples, and highlight its specialized contributions compared to general-purpose graph libraries. |
| title | chipfiring: A Python Package for Efficient Mathematical Analysis of Chip-Firing Games on Multigraphs |
| topic | Combinatorics Computational Geometry Mathematical Software Algebraic Geometry |
| url | https://arxiv.org/abs/2508.00269 |