On the Sandpile Group of Dual Graphs

The group of recurrent configurations in the sandpile model, introduced by Dhar , may be considered as a finite abelian group associated with any graph G; we call it the sandpile group of G. The aim of this paper is to prove that the sandpile group of planar graph is isomorphic to that of its dual. A combinatorial point of view on the subject is also developed.