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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Bigraphical arrangements
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by Sam Hopkins and David Perkinson PDF
Trans. Amer. Math. Soc. 368 (2016), 709-725 Request permission

Abstract:

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 in 1996. We also give bounds on the number of regions of a bigraphical arrangement.
References
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Additional Information
  • Sam Hopkins
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Email: shopkins@mit.edu
  • David Perkinson
  • Affiliation: Department of Mathematics, Reed College, Portland, Oregon 97202
  • Email: davidp@reed.edu
  • Received by editor(s): December 23, 2012
  • Received by editor(s) in revised form: December 3, 2013
  • Published electronically: April 23, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 709-725
  • MSC (2010): Primary 52C35; Secondary 05C25
  • DOI: https://doi.org/10.1090/tran/6341
  • MathSciNet review: 3413881