Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

The shuffle conjecture


Author: Stephanie van Willigenburg
Journal: Bull. Amer. Math. Soc. 57 (2020), 77-89
MSC (2010): Primary 05E05, 05E10, 20C30
DOI: https://doi.org/10.1090/bull/1672
Published electronically: July 1, 2019
Full-text PDF
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

Abstract: Walks in the plane taking unit-length steps north and east from $ (0,0)$ to $ (n,n)$ never dropping below $ y=x$ and parking cars subject to preferences are two intriguing ingredients in a formula conjectured in 2005, now famously known as the shuffle conjecture.

Here we describe the combinatorial tools needed to state the conjecture. We also give key parts and people in its history, including its eventual algebraic solution by Carlsson and Mellit, which was published in the Journal of the American Mathematical Society in 2018. Finally, we conclude with some remaining open problems.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2010): 05E05, 05E10, 20C30

Retrieve articles in all journals with MSC (2010): 05E05, 05E10, 20C30


Additional Information

Stephanie van Willigenburg
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Email: steph@math.ubc.ca

DOI: https://doi.org/10.1090/bull/1672
Received by editor(s): February 6, 2019
Published electronically: July 1, 2019
Additional Notes: The author was supported in part by the National Sciences and Engineering Research Council of Canada and in part by funding from the Simons Foundation and the Centre de Recherches Mathématiques, through the Simons–CRM scholar-in-residence program
Dedicated: On the occasion of Adriano Garsia’s 90th birthday
Article copyright: © Copyright 2019 American Mathematical Society