ABSTRACT

This chapter looks at some aspects of the Tutte polynomial that result from considering different methods of topplings when applying the burning test to recurrent configurations. It presents three different toppling schedules and the corresponding deterministic algorithms for the burning test. The first toppling schedule is a naive choice, which illustrates simply how to construct a corresponding spanning tree, but this correspondence is not necessarily bijective. The second toppling schedule is attributed to Dhar and Majumdar and is called the parallel update burning test. The third toppling schedule is attributed to Cori and Le Borgne and relates the sandpile model to an evaluation of the classical Tutte polynomial: up to a constant, the distribution of the number of nonsink grains on recurrent configurations is also the distribution of the Tutte external activity on spanning trees.