Janet Dong

collaborators

4 papers

math.CO2024

New refinements of Narayana polynomials and Motzkin polynomials

Janet J. W. Dong, Lora R. Du, Kathy Q. Ji +1

Chen, Deutsch and Elizalde introduced a refinement of the Narayana polynomials by distinguishing between old (leftmost child) and young leaves of plane trees. They also provided a…

math.CO2023

Convexity and log-concavity of the partition function weighted by the parity of the crank

Janet J. W. Dong, Kathy Q. Ji

Let $M_{0} (n)$ (resp. $M_{1} (n)$ ) denote the number of partitions of $n$ with even (reps. odd) crank. Choi, Kang and Lovejoy established an asymptotic formula for $M_{0} (n) - M_{1} (n)$ . By u…

math.CO2023

Unimodality of $k$ -Regular Partitions into Distinct Parts with Bounded Largest Part

Janet J. W. Dong, Kathy Q. Ji

A $k$ -regular partition into distinct parts is a partition into distinct parts with no part divisible by $k$ . In this paper, we provide a general method to establish the unimodalit…

math.CO2023

Unimodality of partition polynomials related to Borwein's conjecture

Janet J. W. Dong, Kathy Q. Ji

The objective of this paper is to prove that the polynomials $\prod_{k = 0}^{n} (1 + q^{3 k + 1}) (1 + q^{3 k + 2})$ are symmetric and unimodal for $n \geq 0$ by an analytical method.

New refinements of Narayana polynomials and Motzkin polynomials

Convexity and log-concavity of the partition function weighted by the parity of the crank

Unimodality of k-Regular Partitions into Distinct Parts with Bounded Largest Part

Unimodality of partition polynomials related to Borwein's conjecture

Unimodality of $k$ -Regular Partitions into Distinct Parts with Bounded Largest Part