Menghao Qu

activity

20232026

collaborators

4 papers

math.CO2026

Schur positivity of nabla on Petrie symmetric functions

Menghao Qu

The Petrie symmetric function $G (k, n)$ , introduced by Grinberg, is defined as the sum of monomial symmetric functions $m_{λ}$ indexed by partitions $λ ⊢ n$ satisfying $λ_{1} < k$ . Th…

math.CO2026

Schur positivity of the nabla operator on two-column modified Hall--Littlewood polynomials

Menghao Qu

Bergeron, Garsia, Haiman, and Tesler (1999) introduced two Schur positivity conjectures concerning the action of the $\nabla$ operator on modified Hall--Littlewood polynomials. Alt…

math.CO2025

Symmetry of the refined $q, t$ -Catalan polynomials for $k$ -Dyck paths

Menghao Qu, Yingrui Zhang

Pappe, Paul, and Schilling introduced two combinatorial statistics, depth and ddinv, associated with classical Dyck paths, and proved that the distributions of (area, depth) and (d…

math.CO2023

A parking function interpretation for $(- 1)^{k} \nabla m_{2^{k} 1^{l}}$

Menghao Qu, Guoce Xin

Haglund, Morse, and Zabrocki introduced a family of creation operators of Hall-Littlewood polynomials, ${C_{a}}$ for any $a \in Z$ , in their compositional refinement of t…

Schur positivity of nabla on Petrie symmetric functions

Schur positivity of the nabla operator on two-column modified Hall--Littlewood polynomials

Symmetry of the refined q,t-Catalan polynomials for k-Dyck paths

A parking function interpretation for (−1)k∇m2k1l​

Symmetry of the refined $q, t$ -Catalan polynomials for $k$ -Dyck paths

A parking function interpretation for $(- 1)^{k} \nabla m_{2^{k} 1^{l}}$