11 papers
Dilated Hankel determinants
Guo-Niu Han
For a sequence we define its dilated Hankel determinant , the minor of the infinite Hankel matri…
-Derivative Grammar
Guo-Niu Han, Kathy Q. Ji, Huan Xiong
Context-free grammars, originating in computer science, are related to enumerative combinatorics through two distinct lines of development pioneered by Schützenberger and Chen, re…
On the distributions of the statistics (des, maj, inv) over several classes of permutations
Guo-Niu Han, Kathy Q. Ji, Huan Xiong
We investigate the joint distribution of the trivariate statistics (des, maj, inv) on classical permutations, Andre permutations of the first and second kinds, and Simsun permutati…
The 1/2-Conjecture for -Binomial Coefficients with Fractional Index
Guo-Niu Han, Huan Xiong
For a nonnegative integer and a rational number , we define the generalized Gaussian binomial coefficient $\qbinom{r+k}{k} = \frac{(q^{r+1}; q)_k}{(q; q)_k}$.…
The inversion number statistic for inversion sequences
Lora R. Du, Guo-Niu Han
Inversion sequences, also known as subexcedant sequences, form a fundamental class of objects in enumerative combinatorics. In this paper, we study the joint distribution of five s…
Inequalities and asymptotics for hook numbers in restricted partitions
William Craig, Madeline Locus Dawsey, Guo-Niu Han
In this paper, we consider the asymptotic properties of hook numbers of partitions in restricted classes. More specifically, we compare the frequency with which partitions into odd…