European Journal of Combinatorics
External and internal elements of a matroid basis
Discrete Mathematics
On the Möbius algebra of geometric lattices
European Journal of Combinatorics
Chip-Firing and the Critical Group of a Graph
Journal of Algebraic Combinatorics: An International Journal
On the sandpile group of dual graphs
European Journal of Combinatorics
Polynomial ideals for sandpiles and their Gröbner bases
Theoretical Computer Science
Coding distributive lattices with edge firing games
Information Processing Letters
The sand-pile model and Tutte polynomials
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Liquidity in credit networks: a little trust goes a long way
Proceedings of the 12th ACM conference on Electronic commerce
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We give some new enumerations of indegree sequences of orientations of a graph using the Tutte polynomial. Then we introduce some discrete dynamical systems in digraphs consisting in reversing cycles, cocycles, or both, which extend the edge firing game (reversing sinks) by considering all orientations (reversing cocycles) and by introducing duality (reversing cycles). We show that indegree sequences can represent the configurations of these systems, and we enumerate equivalence classes of these systems. In particular, concerning the cycle-cocycle reversing system, we show that its configurations are in bijection with indegree sequences of orientations having a given vertex (quasi-sink of the system) reachable from any other. We also briefly discuss its generalization to oriented matroids, and relate structural and enumerative properties of its configurations to those of the sandpile model or chip firing game.