Yueming Zhong
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View article: The constant term algebra of type $A$: the Structure
The constant term algebra of type $A$: the Structure Open
In this paper, we discover a new noncommutative algebra. We refer this algebra as the constant term algebra of type $A$, which is generated by certain constant term operators. We characterize a structural result of this algebra by establis…
View article: Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials
Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials Open
In chemistry, Cyvin-Gutman enumerates Kekul\'{e} numbers for certain benzenoids and record it as $A050446$ on OEIS. This number is exactly the two variable array $T(n,m)$ defined by the recursion $T(n, m) = T(n, m-1) + \sum^{\lfloor\frac{n…
View article: A symmetric chain decomposition of $N(m,n)$ of composition
A symmetric chain decomposition of $N(m,n)$ of composition Open
A poset is called a symmetric chain decomposition if the poset can be expressed as a disjoint union of symmetric chains. For positive integers $m$ and $n$, let $N(m,n)$ denote the set of all compositions $α=(α_1,\cdots,α_m)$, with $0\le α_…
View article: On Magic Distinct Labellings of Simple Graphs
On Magic Distinct Labellings of Simple Graphs Open
A magic labelling of a graph $G$ with magic sum $s$ is a labelling of the edges of $G$ by nonnegative integers such that for each vertex $v\in V$, the sum of labels of all edges incident to $v$ is equal to the same number $s$. Stanley gave…
View article: An explicit order matching for $L(3,n)$ from several approaches and its extension for $L(4,n)$
An explicit order matching for $L(3,n)$ from several approaches and its extension for $L(4,n)$ Open
Let $L(m,n)$ denote Young's lattice consisting of all partitions whose Young diagrams are contained in the $m\times n$ rectangle. It is a well-known result that the poset $L(m,n)$ is rank symmetric, rank unimodal, and Sperner. A direct pro…
View article: On Parity Unimodality of $q$-Catalan Polynomials
On Parity Unimodality of $q$-Catalan Polynomials Open
A polynomial $A(q)=\sum_{i=0}^n a_iq^i$ is said to be unimodal if $a_0\leqslant a_1\leqslant \cdots \leqslant a_k\geqslant a_{k+1} \geqslant \cdots \geqslant a_n$. We investigate the unimodality of rational $q$-Catalan polynomials, which i…
View article: On Parity Unimodality of $q$-Catalan Polynomials
On Parity Unimodality of $q$-Catalan Polynomials Open
A polynomial $A(q)=\sum_{i=0}^n a_iq^i$ is said to be unimodal if $a_0\le a_1\le \cdots \le a_k\ge a_{k+1} \ge \cdots \ge a_n$. We investigate the unimodality of rational $q$-Catalan polynomials, which is defined to be $C_{m,n}(q)= \frac{1…