Dun Qiu

collaborators

5 papers

math.CO2026

The Ehrhart series of magic squares of orders seven and eight

Dun Qiu, Guoce Xin, Zihao Zhang

Let $IMS_{n} (m)$ count the $n \times n$ nonnegative integer matrices whose row sums, column sums, main-diagonal sum, and antidiagonal sum are all $m$ . We determine the Ehrhar…

math.CO2026

The Schur positivity of $\nabla m_{I^} ¼$

Dun Qiu, Minhao Zhang

Bergeron, Garsia, Haiman and Tesler conjectured in 1999 that, for all partitions $I^¼, I^» ⊢ n$ , the polynomial $(- 1)^{∣ I^¼∣ - ℓ (I^¼)} ⟨ \nabla m_{I^} ¼, s_{I^} » ⟩$ has nonnegat…

math.CO2026

The nonsymmetric compositional Delta theorem

Dun Qiu, Minhao Zhang

Extending the symmetric framework of D'Adderio and Mellit, we establish a nonsymmetric generalization of the compositional Delta theorem. Building on Blasiak et al.'s theory of fla…

math.CO2026

On shortening universal words for multi-dimensional permutations

Sergey Kitaev, Dun Qiu

A universal word (u-word) for $d$ -dimensional permutations of length $n$ is a 2-dimensional word with $d - 1$ rows, any size $n$ window of which is order-isomorphic to exactly one pe…

math.CO2026

Symmetric statistics on rational Dyck paths

Lilan Dai, Shishuo Fu, Dun Qiu

Rational Dyck paths are the rational generalization of classical Dyck paths. They play an important role in Catalan combinatorics, and have multiple applications in algebra and geo…

The Ehrhart series of magic squares of orders seven and eight

The Schur positivity of ∇mI^​¼

The nonsymmetric compositional Delta theorem

On shortening universal words for multi-dimensional permutations

Symmetric statistics on rational Dyck paths

The Schur positivity of $\nabla m_{I^} ¼$