Frank Z. K. Li

collaborators

3 papers

math.CO2022

Combinatorial proofs on the joint distribution of descents and inverse descents

Frank Z. K. Li, Xunhao Liu

Let $A_{n, i, j}$ be the number of permutations on $[n]$ with $(i - 1)$ descents and $(j - 1)$ inverse descents.Carlitz, Roselle and Scoville in 1966 first revealed some combinatorial an…

math.CO2018

Joint Distributions of Permutation Statistics and the Parabolic Cylinder Functions

Amy M. Fu, Frank Z. K. Li

In this paper, we introduce a context-free grammar $G\colon x \rightarrow xy,\, y \rightarrow zu,\, z \rightarrow zw,\, w \rightarrow xv,\, u \rightarrow xyz^{-1}v,\, v \rightarrow…

math.CO2018

Combinatorial proofs for identities related to generalizations of the mock theta functions $ω (q)$ and $ν (q)$

Frank Z. K. Li, Jane Y. X. Yang

The two partition functions $p_{ω} (n)$ and $p_{ν} (n)$ were introduced by Andrews, Dixit and Yee, which are related to the third order mock theta functions $ω (q)$ and $ν (q)$ , respective…

Combinatorial proofs on the joint distribution of descents and inverse descents

Joint Distributions of Permutation Statistics and the Parabolic Cylinder Functions

Combinatorial proofs for identities related to generalizations of the mock theta functions ω(q) and ν(q)

Combinatorial proofs for identities related to generalizations of the mock theta functions $ω (q)$ and $ν (q)$