13 citations · 58 across the 21 of their papers we have counts for
22 papers
The Theta Conjecture
Giovanni Interdonato, Alessandro Iraci
We define a diagonal-inversion statistic on labeled Dyck paths carrying both decorated rises and decorated contractible valleys. This gives an explicit candidate for a bivariate re…
Leaving the Hall: explicit formulas for Negut operators
Michele D'Adderio, Giovanni Interdonato, Alessandro Iraci +1
Recent major breakthroughs in -combinatorics include the introduction of the Dyck path algebra by Carlsson and Mellit and of the Catalanimals by Blasiak et…
A Proof of the Symmetric Theta Conjecture when q = 0
Alessandra Caraceni, Alessandro Iraci
In 10.1093/imrn/rnac258, the authors conjecture a combinatorial formula for the expressions , known as Symmetric Theta Trees Conjecture, in terms of tiered trees…
Shuffle theorems and sandpiles
Michele D'Adderio, Mark Dukes, Alessandro Iraci +3
We provide an explicit description of the recurrent configurations of the sandpile model on a family of graphs , which we call clique-independent graphs, indexed…
Smirnov words and the Delta Conjectures
Alessandro Iraci, Philippe Nadeau, Anna Vanden Wyngaerd
We provide a combinatorial interpretation of the symmetric function in terms of segmented Smirnov words. The motivation for this…
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…
Charmed roots and the Kroweras complement
Benjamin Dequêne, Gabriel Frieden, Alessandro Iraci +3
Although both noncrossing partitions and nonnesting partitions are uniformly enumerated for Weyl groups, the exact relationship between these two sets of combinatorial objects rema…
Some consequences of the valley Delta conjectures
Michele D'Adderio, Alessandro Iraci
In (Haglund, Remmel, Wilson 2018) Haglund, Remmel and Wilson introduced their Delta conjectures, which give two different combinatorial interpretations of the symmetric function $Δ…
Rectangular analogues of the square paths conjecture and the univariate Delta conjecture
Alessandro Iraci, Roberto Pagaria, Giovanni Paolini +1
In this paper, we extend the rectangular side of the shuffle conjecture by stating a rectangular analogue of the square paths conjecture. In addition, we describe a set of combinat…
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…
A proof of the fermionic Theta coinvariant conjecture
Alessandro Iraci, Brendon Rhoades, Marino Romero
Let be a list of commuting variables, be a list of anticommuting variables, and $\mathbb{C}[X_n,…
"Pushing" our way from the valley Delta to the generalised valley Delta
Alessandro Iraci, Anna Vanden Wyngaerd
In [Haglund, Remmel, Wilson 2018] the authors state two versions of the so called Delta conjecture, the rise version and the valley version. Of the former, they also give a more ge…
Decorated Dyck paths, polyominoes, and the Delta conjecture
Michele D'Adderio, Alessandro Iraci, Anna Vanden Wyngaerd
We discuss the combinatorics of decorated Dyck paths and decorated parallelogram polyominoes, extending to the decorated case the main results of both [Haglund 2004] and [Aval et a…
A valley version of the Delta square conjecture
Alessandro Iraci, Anna Vanden Wyngaerd
Inspired by [Qiu, Wilson 2019] and [D'Adderio, Iraci, Vanden Wyngaerd 2019 - Delta Square], we formulate a generalised Delta square conjecture (valley version). Furthermore, we use…
Theta operators, refined Delta conjectures, and coinvariants
Michele D'Adderio, Alessandro Iraci, Anna Vanden Wyngaerd
We introduce the family of Theta operators indexed by symmetric functions that allow us to conjecture a compositional refinement of the Delta conjecture of Haglund, Remme…
The new dinv is not so new
Michele D'Adderio, Alessandro Iraci
In (Duane, Garsia, Zabrocki 2013) the authors introduced a new dinv statistic, denoted ndinv, on the two part case of the shuffle conjecture (Haglund et al. 2005) in order to prove…
The generalized Delta conjecture at t=0
Michele D'Adderio, Alessandro Iraci, Anna Vanden Wyngaerd
We prove the cases q=0 and t=0 of the generalized Delta conjecture of Haglund, Remmel and Wilson involving the symmetric function . Our theorem generalize…
The Delta square conjecture
Michele D'Adderio, Alessandro Iraci, Anna Vanden Wyngaerd
We conjecture a formula for the symmetric function in terms of decorated partially labelled square paths. This can be seen as a gene…
The Schröder case of the generalized Delta conjecture
Michele D'Adderio, Alessandro Iraci, Anna Vanden Wyngaerd
We prove the Schröder case, i.e. the case , of the conjecture of Haglund, Remmel and Wilson (Haglund et al. 2018) for i…
Parallelogram polyominoes, partially labelled Dyck paths, and the Delta conjecture (FULL VERSION)
Michele D'Adderio, Alessandro Iraci
We introduce area, bounce and dinv statistics on decorated parallelogram polyominoes, and prove that some of their q,t-enumerators match $\langle Δ_{h_m} e_{n+1},s_{k+1,1^{n-k}}\ra…
Parallelogram polyominoes, partially labelled Dyck paths, and the Delta conjecture
Michele D'Adderio, Alessandro Iraci
We introduce area, bounce and dinv statistics on decorated parallelogram polyominoes, and prove that some of their q,t-enumerators match $\langle Δ_{h_m} e_{n+1}, s_{k+1,1^{n-k}} \…