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Divisors and sandpiles : an introduction to chip-firing

Author: Scott Corry; David Perkinson
Publisher: Providence, Rhode Island : American Mathematical Society, [2018] ©2018
Series: AMS Non-Series Monographs, volume 114
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Provides an introduction to the combinatorial theory of chip-firing on finite graphs. Part 1 motivates the study of the discrete Laplacian by introducing the dollar game. Part 2 focuses on sandpiles.  Read more...

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Document Type: Book
All Authors / Contributors: Scott Corry; David Perkinson
ISBN: 9781470442187 1470442183
OCLC Number: 1029075672
Description: xiv, 325 pages : illustrations ; 26 cm
Contents: Part 1. Divisors. The dollar game ; The Laplacian ; Algorithms for winning ; Acyclic orientations ; Riemann-Roch --
Part 2. Sandpiles. The sandpile group ; Burning and duality ; Threshold density --
Part 3. Topics. Trees ; Harmonic morphisms ; Divisors on complete graphs ; More about sandpiles ; Cycles and cuts ; Matroids and the Tutte polynomial ; Higher dimensions --
Appendices. Appendix A. Undirected multigraphs ; Directed multigraphs --
Appendix B. Monoids, groups, rings, and fields ; Modules.
Series Title: AMS Non-Series Monographs, volume 114
Responsibility: Scott Corry, David Perkinson.

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