7 citations · 19 across the 9 of their papers we have counts for
8 papers · 1 filter
The super nabla operator
François Bergeron, Jim Haglund, Alessandro Iraci +1
We consider here a new operator, called ``super nabla'', which is shown to be generic among operators for which the modified Macdonald polynomials are joint eigenfunctions. All pre…
Delta and Theta Operator Expansions
Alessandro Iraci, Marino Romero
We give an elementary symmetric function expansion for and when in terms of what we call -parking functions and lattice $…
Tiered trees and Theta operators
Michele D'Adderio, Alessandro Iraci, Yvan LeBorgne +2
In [Dugan-Glennon-Gunnells-Steingrimsson-2019], the authors introduce tiered trees to define combinatorial objects counting absolutely indecomposable representations of certain qui…
Kronecker powers of harmonics, polynomial rings, and generalized principal evaluations
Marino Romero
Our main goal is to compute the decomposition of arbitrary Kronecker powers of the Harmonics of . To do this, we give a new way of decomposing the character for the action of…
New identities for Theta operators
Michele D'Adderio, Marino Romero
In this article, we prove a new general identity involving the Theta operators introduced by the first author and his collaborators in [D'Adderio, Iraci, Vanden Wyngaerd 2020]. Fro…
A proof of the Theta Operator Conjecture
Marino Romero
In the context of the (generalized) Delta Conjecture and its compositional form, D'Adderio, Iraci, and Wyngaerd recently stated a conjecture relating two symmetric function operato…
-Positivity Results and Conjectures
Adriano M. Garsia, James Haglund, Dun Qiu +1
In a 2016 ArXiv posting F. Bergeron listed a variety of symmetric functions with the property that is -positive. A large subvariety of his examples could be…
The Delta Conjecture at
Marino Romero
We use a weight-preserving, sign-reversing involution to find a combinatorial expansion of at in terms of the elementary symmetric function basis. We then use a…