The sandpile model on the complete split graph, Motzkin words, and tiered parking functions

DOI10.1016/j.jcta.2021.105418zbMath1459.05350arXiv2006.08006OpenAlexW3127291652MaRDI QIDQ2229180

Mark Dukes

Publication date: 22 February 2021

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.08006

zbMATH Keywords

complete split graphsandpile modelparking functionschip-firingMotzkin words

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Group actions on combinatorial structures (05E18)

Related Items (1)

Combinatorial aspects of sandpile models on wheel and Fan graphs

Cites Work

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• Two operators on sandpile configurations, the sandpile model on the complete bipartite graph, and a cyclic lemma
• On the sandpile group of dual graphs
• EW-tableaux, Le-tableaux, tree-like tableaux and the abelian sandpile model
• Decomposing recurrent states of the Abelian sandpile model
• Enumeration of \((p,q)\)-parking functions
• Polygon dissections and standard Young tableaux
• Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a \(q,t\)-Narayana polynomial
• Permutation graphs and the abelian sandpile model, tiered trees and non-ambiguous binary trees
• The abelian sandpile model on Ferrers graphs -- a classification of recurrent configurations
• Statistics on parallelogram polyominoes and a \(q,t\)-analogue of the Narayana numbers
• Trees, parking functions, syzygies, and deformations of monomial ideals

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