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Combinatorics of the Diagonal Harmonics

  • Angela HicksEmail author
Chapter
Part of the Association for Women in Mathematics Series book series (AWMS, volume 16)

Abstract

The Shuffle Theorem, recently proven by Carlsson and Mellit, states that the bigraded Frobenius characteristic of the diagonal harmonics is equal to a weighted sum of parking functions. In this introduction to the topic, we discuss the theorem and connections between it and the well-known Macdonald polynomials. Furthermore, we describe important combinatorial bijections which imply various restatements of the theorem and play an important role in its proof. Finally, we briefly discuss the proof and describe various generalizations of the theorem.

Notes

Acknowledgements

The author would like to express her gratitude for the many helpful remarks of the anonymous reviewer.

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Copyright information

© The Author(s) and the Association for Women in Mathematics 2019

Authors and Affiliations

  1. 1.Lehigh UniversityBethlehemUSA

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