Title

The Valley Version of the Extended Delta Conjecture

Published In

Journal of Combinatorial Theory Series A

Document Type

Citation

Publication Date

10-1-2020

Abstract

The Shuffle Theorem of Carlsson and Mellit gives a combinatorial expression for the bigraded Frobenius characteristic of the ring of diagonal harmonics, and the Delta Conjecture of Haglund, Remmel and the second author provides two generalizations of the Shuffle Theorem to the delta operator expression .

Δek′en">Δek′en

Haglund et al. also propose the Extended Delta Conjecture for the delta operator expression

Δek′Δhren">Δek′Δhren

, , which is analogous to the rise version of the Delta Conjecture. Recently, D'Adderio, Iraci and Wyngaerd proved the rise version of the Extended Delta Conjecture at the case when . In this paper, we propose a new valley version of the Extended Delta Conjecture. Then, we work on the combinatorics of extended ordered multiset partitions to prove that the two conjectures for

Δek′Δhren">Δek′Δhren

a are equivalent when t or q equals 0, thus proving the valley version of the Extended Delta Conjecture when t or q equals 0.

Rights

© 2020 Elsevier Inc. All rights reserved.

DOI

10.1016/j.jcta.2020.105271

Persistent Identifier

https://archives.pdx.edu/ds/psu/34230

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