23 citations · 76 across the 24 of their papers we have counts for
10 papers · 1 filter
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…
The Poincaré polynomial of the type B analogue of
Luis Ferroni, Roberto Pagaria, Lorenzo Vecchi
We establish formulas for the Poincaré polynomial of the type B analogue of the Deligne--Knudsen--Mumford moduli space of rational curves with marked points, providing type B c…
Falling stars: a fall-decorated rational shuffle theorem
Alessandro Iraci, Roberto Pagaria, Giovanni Paolini
In this paper, we formulate a rational analog of the fall Delta theorem and the Delta square conjecture. We find a new dinv statistic on fall-decorated paths on a $(m+k) \times (n+…
Elliptic arrangements of complex multiplication type
Luca Moci, Roberto Pagaria, Maddalena Pismataro +1
We provide a natural definition of an elliptic arrangement, extending the classical framework to an elliptic curve E with complex multiplication. We analyse the intersections of el…
Building sets, Chow rings, and their Hilbert series
Christopher Eur, Luis Ferroni, Jacob P. Matherne +2
We establish formulas for the Hilbert series of the Chow ring of a polymatroid using arbitrary building sets. For braid matroids and minimal building sets, our results produce new…
Inductive and divisional posets
Roberto Pagaria, Maddalena Pismataro, Tan Nhat Tran +1
We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we in…
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…
Representations of torsion-free arithmetic matroids
Roberto Pagaria, Giovanni Paolini
We study the representability problem for torsion-free arithmetic matroids. By using a new operation called "reduction" and a "signed Hermite normal form", we provide and implement…
Orientable arithmetic matroids
Roberto Pagaria
The theory of matroids has been generalized to oriented matroids and, recently, to arithmetic matroids. We want to give a definition of "oriented arithmetic matroid" and prove some…
Two Examples of Toric Arrangements
Roberto Pagaria
We show that the integral cohomology algebra of the complement of a toric arrangement is not determined by the poset of layers. Moreover, the rational cohomology algebra is not det…