Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Qiu Dun"'
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 states that the incomparability graph of the boolean algebra $B_n$ is
Externí odkaz:
http://arxiv.org/abs/2408.13127
Autor:
Kitaev, Sergey, Qiu, Dun
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 permutations of length $n$ are covered. It is known that u-cycles for perm
Externí odkaz:
http://arxiv.org/abs/2408.05984
Publikováno v:
Journal of Integer Sequences, Vol. 26 (2023), Article 23.4.2
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 classical 132- or 213-avoidance restriction on the permutations, we recover
Externí odkaz:
http://arxiv.org/abs/2201.08168
Autor:
Qiu, Dun, Wilson, Andrew Timothy
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 Haglund, Remmel and the second author provides two generalizations of
Externí odkaz:
http://arxiv.org/abs/1907.00268
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 explained by the conjecture that the Dyck path LLT polynomials exhibit
Externí odkaz:
http://arxiv.org/abs/1904.07912
Autor:
Qiu, Dun, Remmel, Jeffrey
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol. 21 no. 2, Permutation Patters 2018, Permutation Patterns (November 4, 2019) dmtcs:5088
Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set o
Externí odkaz:
http://arxiv.org/abs/1810.10099
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 $\mathcal{S}_n(123)$ and $\mathcal{S}_n(132)$. We first study the distribution of consecuti
Externí odkaz:
http://arxiv.org/abs/1809.01384
Autor:
Qiu, Dun, Remmel, Jeffrey
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 given by the Hikita polynomial ${H}_{m,n}[X;q,t]$. Later, Bergeron-Garsi
Externí odkaz:
http://arxiv.org/abs/1806.04348
Autor:
Qiu, Dun, Remmel, Jeffrey
An ordered set partition of $\{1,2,\ldots,n\}$ is a partition with an ordering on the parts. Let $\mathcal{OP}_{n,k}$ be the set of ordered set partitions of $[n]$ with $k$ blocks. Godbole, Goyt, Herdan and Pudwell defined $\mathcal{OP}_{n,k}(\sigma)
Externí odkaz:
http://arxiv.org/abs/1804.07087
Let $\mathbb{N}$ denote the set of non-negative integers. Haglund, Wilson, and the second author have conjectured that the coefficient of any Schur function $s_\lambda[X]$ in $\Delta_{e_k} e_n[X]$ is a polynomial in $\mathbb{N}[q,t]$. We present four
Externí odkaz:
http://arxiv.org/abs/1710.03340