## 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