WebDec 29, 2024 · A chip-firing game on a vertex-weighted graph \Gamma is a one-player game where a move amounts to selecting a vertex and firing it, i.e., redistributing the … WebA variant of the chip-firing game on a graph is defined. It is shown that the set of configurations that are stable and recurrent for this game can be given the structure of an abelian group, and that the order of the group is equal to the tree number of the graph. In certain cases the game can be used to illuminate the structure of the group.
Chip-Firing Games SpringerLink
WebAug 12, 2024 · Chip-Firing Games and Critical Groups. Darren Glass, Nathan Kaplan. In this expository article intended to be accessible to undergraduate students we introduce a finite abelian group that can be associated to any finite connected graph. This group can be defined in an elementary combinatorial way in terms of chip-firing operations, and has … WebThe chip-firing game is a one-player game on a graph which was invented around 1983 and since has become an important part of the study of structural combina... how change your signature in outlook
The Mathematics of Chip-Firing - Wikipedia
The chip-firing game is a one-player game on a graph which was invented around 1983 and since has become an important part of the study of structural combinatorics. Each vertex has the number of tokens indicated by its state variable. On each firing, a vertex is selected and one of its tokens is … See more Let the finite graph G be connected and loopless, with vertices V = {1, 2, . . . , n}. Let deg(v) be the degree of a vertex, and e(v,w) the number of edges between vertices v and w. A configuration or state of the game is … See more Some chip-firing games, known as dollar games, interpret the chips as dollars and the vertices as money borrowers and lenders. Two variants of dollar game are prominent in the literature: Baker and Norine's variant In this dollar game, … See more • Abelian sandpile model • The Mathematics of Chip-Firing • Riemann–Roch theorem See more • MIT Course 18.312: Algebraic Combinatorics • Weisz Ágoston: A koronglövő játék. Szakdolgozat, ELTE TTK Bsc, 2014 See more WebOct 25, 2024 · Chip-firing games, Jacobians, and Prym varieties. Yoav Len. These notes are a self-contained introduction to the theory of chip-firing games on metric graphs, as … WebJul 25, 2024 · This Demonstration shows a chip-firing game, which is also referred to as an Abelian sandpile model. Starting with a simple weighted directed graph and a number of chips to be distributed among the vertices of , a new graph is constructed with a vertex for each distribution of chips and an edge corresponding to each valid chip firing. how many photos does 15gb hold