MathOverflow Asked by castor on February 16, 2021
In the paper "On the Sandpile Group of a Graph" by Cori and Rossin one can find a result related to the structure of the sandpile group of $W_n$. Is there a way to provide a set of generators in parametric form in both the cases when $n$ is even/odd?
Update #1: the identity is known (source is coming), that is the all 2’s configuration. Numerical experience suggests that in case of even values of $n$ two configurations generating the group are $(1,2,1,ldots),(2,1,1,ldots),$ in case of odd values these are $(2,1,1,ldots),(2,2,1,ldots).$ Probably it is also known, however I have not found yet.
Update #2: Biggs: "Chip-Firing and the Critical Group of a Graph" provides generators as well.
As noted above Biggs described the structure of $W_n$ and provided also generators in case of $n$ is odd, see Theorem 9.2 in "Chip-Firing and the Critical Group of a Graph". The even case is considered as well.
Correct answer by castor on February 16, 2021
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