Dun Qiu

activity

20172026

most citedQuadrant marked mesh patterns in 123-avoiding permutations

8 citations · 19 across the 16 of their papers we have counts for

collaborators

19 papers

math.CO2026

The nabla operator, Hall--Littlewood polynomials and LLT polynomials

Feng Gu, Mingyang Kang, Dun Qiu +1

Bergeron, Garsia, Haiman, and Tesler conjectured that $(- 1)^{n - ℓ (μ)} \nabla H_{μ} [X; 0, t]$ and $\nabla ω H_{μ} [X; 0, t^{- 1}]$ are Schur positive, and that $\nablaω\wi…

math.CO2026

The $(k m, k n)$ -square paths theorem

Dun Qiu, Minhao Zhang

For positive integers $k, m, n$ with $g cd (m, n) = 1$ , we prove a $(k m, k n)$ -square paths theorem: the symmetric function $(- 1)^{k - 1} \frac{[ k m ] _{q}}{[ k ] _{q}} p_{k} [- M X^{m, n}] \cdot 1$ is a weight…

math.CO2026

Coincidences and Growth of Boxed Mesh Patterns

Sergey Kitaev, Dun Qiu, Chao Xu

A boxed mesh pattern is a mesh pattern whose selected entries lie in an empty axis-parallel rectangle. We classify coincidences of boxed patterns with classical and vincular patter…

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 $\nabla m_{μ}$

Dun Qiu, Minhao Zhang

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

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.CO2025

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…

math.CO2024

Stanley's conjecture on the Schur positivity of distributive lattices

Grace M. X. Li, Dun Qiu, Arthur L. B. Yang +1

In this paper we solve an open problem on distributive lattices, which was proposed by Stanley in 1998. This problem was motivated by a conjecture due to Griggs, which equivalently…

math.CO2024★ 1 cited

On a family of universal cycles for multi-dimensional permutations

Sergey Kitaev, Dun Qiu

A universal cycle (u-cycle) for permutations of length $n$ is a cyclic word, any size $n$ window of which is order-isomorphic to exactly one permutation of length $n$ , and all perm…

math.CO2022

Pattern-avoidance and Fuss-Catalan numbers

Per Alexandersson, Samuel Asefa Fufa, Frether Getachew +1

We study a subset of permutations, where entries are restricted to having the same remainder as the index, modulo some integer $k \geq 2$ . We show that when also imposing the class…

math.CO2019

The valley version of the Extended Delta Conjecture

Dun Qiu, Andrew Timothy Wilson

The Shuffle Theorem of Carlsson and Mellit gives a combinatorial expression for the bigraded Frobenius characteristic of the ring of diagonal harmonics, and the Delta Conjecture of…

math.CO2019★ 7 cited

$e$ -Positivity Results and Conjectures

Adriano M. Garsia, James Haglund, Dun Qiu +1

In a 2016 ArXiv posting F. Bergeron listed a variety of symmetric functions $G [X; q]$ with the property that $G [X; 1 + q]$ is $e$ -positive. A large subvariety of his examples could be…

math.CO2018

Classical pattern distributions in $S_{n} (132)$ and $S_{n} (123)$

Dun Qiu, Jeffrey Remmel

Classical pattern avoidance and occurrence are well studied in the symmetric group $S_{n}$ . In this paper, we provide explicit recurrence relations to the generating func…

math.CO2018

Counting Consecutive Pattern Matches in $S_{n} (132)$ and $S_{n} (123)$

Ran Pan, Dun Qiu, Jeffrey Remmel

In this paper, we study the distribution of consecutive patterns in the set of 123-avoiding permutations and the set of 132-avoiding permutations, that is, in $S_{n} (123)$ …

math.CO2018

Schur Function Expansions and the Rational Shuffle Theorem

Dun Qiu, Jeffrey Remmel

Gorsky and Negut introduced operators $Q_{m, n}$ on symmetric functions and conjectured that, in the case where $m$ and $n$ are relatively prime, the expression $Q_{m, n} (1)$ is gi…

math.CO2018★ 2 cited

Patterns in words of ordered set partitions

Dun Qiu, Jeffrey Remmel

An ordered set partition of ${1, 2, \dots, n}$ is a partition with an ordering on the parts. Let $O P_{n, k}$ be the set of ordered set partitions of $[n]$ with $k$ blocks.…

math.CO2017★ 1 cited

On the Schur positivity of $Δ_{e_{2}} e_{n} [X]$

Dun Qiu, Jeffrey B. Remmel, Emily Sergel +1

Let $N$ denote the set of non-negative integers. Haglund, Wilson, and the second author have conjectured that the coefficient of any Schur function $s_{λ} [X]$ in $Δ_{e_k} e_…

math.CO2017★ 8 cited

Quadrant marked mesh patterns in 123-avoiding permutations

Dun Qiu, Jeffrey B. Remmel

Given a permutation $σ = σ_{1} \dots σ_{n}$ in the symmetric group $S_{n}$ , we say that $σ_{i}$ matches the quadrant marked mesh pattern $MMP (a, b, c, d)$ in $σ$ if there…

The nabla operator, Hall--Littlewood polynomials and LLT polynomials

The (km,kn)-square paths theorem

Coincidences and Growth of Boxed Mesh Patterns

The Ehrhart series of magic squares of orders seven and eight

The Schur positivity of ∇mμ​

The nonsymmetric compositional Delta theorem

On shortening universal words for multi-dimensional permutations

Symmetric statistics on rational Dyck paths

Stanley's conjecture on the Schur positivity of distributive lattices

On a family of universal cycles for multi-dimensional permutations

Pattern-avoidance and Fuss-Catalan numbers

The valley version of the Extended Delta Conjecture

e-Positivity Results and Conjectures

Classical pattern distributions in Sn​(132) and Sn​(123)

Counting Consecutive Pattern Matches in Sn​(132) and Sn​(123)

Schur Function Expansions and the Rational Shuffle Theorem

Patterns in words of ordered set partitions

On the Schur positivity of Δe2​​en​[X]

Quadrant marked mesh patterns in 123-avoiding permutations

The $(k m, k n)$ -square paths theorem

The Schur positivity of $\nabla m_{μ}$

$e$ -Positivity Results and Conjectures

Classical pattern distributions in $S_{n} (132)$ and $S_{n} (123)$

Counting Consecutive Pattern Matches in $S_{n} (132)$ and $S_{n} (123)$

On the Schur positivity of $Δ_{e_{2}} e_{n} [X]$