Séminaire Lotharingien de Combinatoire, B77h (2018), 48 pp.
Michele D'Adderio and Yvan Le Borgne
The Sandpile Model on Km,n and the Rank of its Configurations
We present an algorithm to compute the rank of a configuration of the
sandpile model for the complete bipartite graph Km,n of
complexity O(m+n). Furthermore, we provide a formula for the generating function of parking sorted configurations on complete bipartite graphs Km,n according to
rank, degree, and the sizes m and n.
The results in the present
paper are similar to those found in a previous paper by Cori and
[Electron. J. Combin. 23(1) (2016), Paper 1.31, 47 pp.]
for the complete graph
Kn+1, and they rely on the analysis of certain operators on
the stable sorted configurations of Km,n developed by
Aval, D'Adderio, Dukes and Le Borgne in
[Adv. Appl. Math. 73 (2016), 59-98].
Received: October 20, 2016.
Revised: April 17, 2017.
Accepted: January 13, 2017.
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