Parallelogram polyominoes and rectangular EW-tableaux: Correspondences through the Sandpile model

DOI10.54550/ECA2021V1S1R8zbMath1491.05027arXiv2007.15932OpenAlexW3209430789MaRDI QIDQ5093425

Amal Alofi, Mark Dukes

Publication date: 26 July 2022

Published in: Enumerative Combinatorics and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.15932

zbMATH Keywords

parallelogram polyominoessandpile modelbijective combinatoricsEW-tableaux

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19)

Related Items (1)

Combinatorial aspects of sandpile models on wheel and Fan graphs

Cites Work

• Two operators on sandpile configurations, the sandpile model on the complete bipartite graph, and a cyclic lemma
• The sand-pile model and Tutte polynomials
• 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
• Enumerative properties of Ferrers graphs
• Enumeration of \((p,q)\)-parking functions
• 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
• Course 14 Mathematical aspects of the Abelian Sandpile model
• Poly-Bernoulli Numbers and Eulerian Numbers
• Restricted lonesum matrices

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