Hai Zhu

collaborators

6 papers

math.CO2026

Rook placements and orbit harmonics

Hai Zhu

For fixed positive integers $n, m$ , let $Mat_{n \times m} (C)$ be the affine space consisting of all $n \times m$ complex matrices, and let $\mathbb{C}[\mathbf{x}_{n\…

math.CO2026

Plethysm and orbit harmonics

Hai Zhu

Let $I^_{(b^{a})}$ be the locus of unordered set partitions of $[ab]$ with $a$ blocks of size $b$ . We embed unordered set partitions of $[n]$ into the affine space $\mathbb{C}^{\bino…

math.CO2025

An extension of Viennot's shadow to rook placements via orbit harmonics

Jasper M. Liu, Hai Zhu

For fixed positive integers $n, m, r$ , let $Mat_{n \times m} (C)$ be the affine space of $n \times m$ complex matrices with coordinate ring $\mathbb{C}[\mathbf{x}_{n…

math.CO2025

Positive combinatorial formulae for involution matrix loci and orbit harmonics

Hai Zhu

Let $M_{n, a}$ be the set consisting of involutions in symmetric group $S_{n}$ with exactly $a$ fixed points and apply the orbit harmonics method to obtain a grad…

math.NT2025

On the properties of alternating invariant functions

Haiqing Zhu, Su Hu, Min-Soo Kim

Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer $n$ }, \end{align*} are named the…

math.CO2024

Involution matrix loci and orbit harmonics

Moxuan J. Liu, Yichen Ma, Brendon Rhoades +1

Let $Mat_{n \times n} (C)$ be the affine space of $n \times n$ complex matrices with coordinate ring $C [x_{n \times n}]$ . We define graded quotie…