The shuffle conjecture

Stephanie van Willigenburg
2019 Bulletin of the American Mathematical Society  
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
more » ... athematical Society in 2018. Finally, we conclude with some remaining open problems.
doi:10.1090/bull/1672 fatcat:o6xy6fs4crbgjeszfkd3imrnmq