Tiered tree, Parking function and Postnikov-Shapiro algebra

2024/08/06 by Biswadeep Bagchi, Bagchi, Biswadeep, Srinibas Swain +1
Computer Science · Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2408.03087

openalex publication_date 2024/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Tiered trees were introduced as a combinatorial object for counting absolutely indecomposable representation of certain quivers and torus orbit of certain homogeneous variety. In this paper, we define a bijection between the set of parallelogram polyominoes and graphical parking functions. Moreover, we defined the space S_G for complete tiered graphs and described tiered graphs in terms of Whitney's operations.

Related

• Tiered trees, weights, and q-Eulerian numbers
• Postnikov-Shapiro Algebras, Graphical Matroids and their generalizations
• Parking trees and the toric g-vector of nestohedra
• Generalized Bijective Maps between G-Parking Functions, Spanning\n Trees, and the Tutte Polynomial
• Bijections Between Multiparking Functions, Dirichlet Configurations, and Descending R-Traversals