Marino Romero

collaborators

4 papers

math.CO2025

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

FabiÃ¡n LevicÃ¡n-SantibÃ¡Ã±ez, 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.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.QA2025

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…

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…

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

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

Tesler identities for wreath Macdonald polynomials

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

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