Sam Hopkins ; David Perkinson - Bigraphical arrangements

dmtcs:2398 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2398
Bigraphical arrangements

Authors: Sam Hopkins 1; David Perkinson 2

  • 1 Massachusetts Institute of Technology
  • 2 Reed College

We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson. A consequence is a new proof of a bijection between labeled graphs and regions of the Shi arrangement first given by Stanley. We also give bounds on the number of regions of a bigraphical arrangement. The full version of this paper is forthcoming in the $\textit{Transactions of the American Mathematical Society}$

https://doi.org/10.46298/dmtcs.2398
Source: HAL:hal-01207608v1
Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: hyperplane arrangements,parking functions,abelian sandpile model,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV 0801.1114
Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.disc.2010.01.002
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.0801.1114
  • 0801.1114
  • 10.48550/arxiv.0801.1114
  • 10.1016/j.disc.2010.01.002
G-parking functions, acyclic orientations and spanning trees

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