3 papers
math.CO2026
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…
math.CO2026
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 $\qbinom{r+k}{k} = \frac{(q^{r+1}; q)_k}{(q; q)_k}$.…
cs.LG2024
Deep ReLU Networks Have Surprisingly Simple Polytopes
Feng-Lei Fan, Wei Huang, Xiangru Zhong +4
A ReLU network is a piecewise linear function over polytopes. Figuring out the properties of such polytopes is of fundamental importance for the research and development of neural…