James Haglund ; Jeffrey B. Remmel ; Andrew Timothy Wilson - The Delta Conjecture

dmtcs:6384 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6384
The Delta ConjectureArticle

Authors: James Haglund 1; Jeffrey B. Remmel 2; Andrew Timothy Wilson 1

  • 1 Department of Mathematics [Philadelphia]
  • 2 Department of Mathematics [Univ California San Diego]

We conjecture two combinatorial interpretations for the symmetric function ∆eken, where ∆f is an eigenoperator for the modified Macdonald polynomials defined by Bergeron, Garsia, Haiman, and Tesler. Both interpretations can be seen as generalizations of the Shuffle Conjecture, a statement originally conjectured by Haglund, Haiman, Remmel, Loehr, and Ulyanov and recently proved by Carlsson and Mellit. We show how previous work of the second and third authors on Tesler matrices and ordered set partitions can be used to verify several cases of our conjectures. Furthermore, we use a reciprocity identity and LLT polynomials to prove another case. Finally, we show how our conjectures inspire 4-variable generalizations of the Catalan numbers, extending work of Garsia, Haiman, and the first author.


Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Combinatorics of Symmetric Functions; Funder: National Science Foundation; Code: 1200296

Publications

IsRelatedTo
  • 1 ScholeXplorer

References

31 Documents citing this article

Consultation statistics

This page has been seen 172 times.
This article's PDF has been downloaded 141 times.