K. Ji

activity

20052023

most citedUnimodality of the Andrews-Garvan-Dyson cranks of partitions

7 citations · 14 across the 23 of their papers we have counts for

collaborators

28 papers

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.

math.CO2023★ 1 cited

Higher Order Turan Inequalities for the Distinct Partition Function

Janet J. W. Dong, Kathy Q. Ji

We prove that the number $q (n)$ of partitions into distinct parts is log-concave for $n \geq 33$ and satisfies the higher order Turán inequalities for $n \geq 121$ conjectured by Cr…

math.CO2022

Turán inequalities for the broken $k$ -diamond partition function

Janet J. W. Dong, Kathy Q. Ji, Dennis X. Q. Jia

We obtain an asymptotic formula for Andrews and Paule's broken $k$ -diamond partition function $Δ_{k} (n)$ where $k = 1$ or $2$ . Based on this asymptotic formula, we derive that $Δ_{k} (n)$ …

math.CO2022★ 1 cited

A Cyclic Analogue of Stanley's Shuffle Theorem

Kathy Q. Ji, Dax T. X. Zhang

We introduce the cyclic major index of a cycle permutation and give a bivariate analogue of enumerative formula for the cyclic shuffles with a given cyclic descent numbers due to A…

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

Higher Order Turan Inequalities for the Distinct Partition Function

Turán inequalities for the broken k-diamond partition function

A Cyclic Analogue of Stanley's Shuffle Theorem

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

Turán inequalities for the broken $k$ -diamond partition function