5 papers
Tesler identities for wreath Macdonald polynomials
Marino Romero, Joshua Jeishing Wen
We give an explicit formula for an operator that sends a wreath Macdonald polynomial to the delta function at a character associated to its partition. This allows us to prove many…
Five-Term Relations for wreath Macdonald polynomials and tableau formulas for Pieri coefficients
Marino Romero, Joshua Jeishing Wen
We present a variety of new identities involving operators in the theory of wreath Macdonald polynomials. One such family of identities gives five-term relations, analogous to the…
On Macdonald expansions of -chromatic symmetric functions and the Stanley-Stembridge Conjecture
Sean T. Griffin, Anton Mellit, Marino Romero +2
The Stanley-Stembridge conjecture asserts that the chromatic symmetric function of a -free graph is -positive. Recently, Hikita proved this conjecture by giving an explic…
Color rules for cyclic wreath products and semigroup algebras from projective toric varieties
Fabián Levicán-Santibáñez, Marino Romero
We introduce the notion of "color rules" for computing class functions of , where is the cyclic group of order and is the symmetric group on letter…
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,…