DOAJ Open Access 2020

The Delta Conjecture

James Haglund Jeffrey B. Remmel Andrew Timothy Wilson

Lihat Sumber DOI

Abstrak

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.

Topik & Kata Kunci

Mathematics

Penulis (3)

James Haglund

Jeffrey B. Remmel

Andrew Timothy Wilson

Format Sitasi

APA MLA BibTeX

Haglund, J., Remmel, J.B., Wilson, A.T. (2020). The Delta Conjecture. https://doi.org/10.46298/dmtcs.6384

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6384

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6384
Akses: Open Access ✓