Marino Romero

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math.CO2025

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…

math.CO2025

On Macdonald expansions of $q$ -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 $(3 + 1)$ -free graph is $e$ -positive. Recently, Hikita proved this conjecture by giving an explic…

math.CO2025

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 $Z_{k} ≀ S_{n}$ , where $Z_{k}$ is the cyclic group of order $k$ and $S_{n}$ is the symmetric group on $n$ letter…

math.CO2022

A proof of the fermionic Theta coinvariant conjecture

Alessandro Iraci, Brendon Rhoades, Marino Romero

Let $(x_{1}, \dots, x_{n}, y_{1}, \dots, y_{n})$ be a list of $2 n$ commuting variables, $(θ_{1}, \dots, θ_{n}, ξ_{1}, \dots, ξ_{n})$ be a list of $2 n$ anticommuting variables, and $\mathbb{C}[X_n,…

Five-Term Relations for wreath Macdonald polynomials and tableau formulas for Pieri coefficients

On Macdonald expansions of q-chromatic symmetric functions and the Stanley-Stembridge Conjecture

Color rules for cyclic wreath products and semigroup algebras from projective toric varieties

A proof of the fermionic Theta coinvariant conjecture

On Macdonald expansions of $q$ -chromatic symmetric functions and the Stanley-Stembridge Conjecture