Tiered tree, Parking function and Postnikov-Shapiro algebra
Biswadeep Bagchi, Srinibas Swain

TL;DR
This paper explores the combinatorial structures of tiered trees, parallelogram polyominoes, and parking functions, establishing bijections and algebraic descriptions to advance understanding of their interrelations.
Contribution
It introduces a bijection between parallelogram polyominoes and graphical parking functions and characterizes tiered graphs using Whitney's operations.
Findings
Established a bijection between parallelogram polyominoes and parking functions.
Defined the space mathcal{S}_G for complete tiered graphs.
Described tiered graphs in terms of Whitney's operations.
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 for complete tiered graphs and described tiered graphs in terms of Whitney's operations.
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Taxonomy
TopicsGraph theory and applications · Matrix Theory and Algorithms · Advanced Topics in Algebra
