53 citations · 144 across the 29 of their papers we have counts for
32 papers
Periodic minimum in the count of binomial coefficients not divisible by a prime
Hsien-Kuei Hwang, Svante Janson, Tsung-Hsi Tsai
The summatory function of the number of binomial coefficients not divisible by a prime is known to exhibit regular periodic oscillations, yet identifying the less regularly behaved…
Analysis of some exactly solvable diminishing urn models
Hsien-Kuei Hwang, Markus Kuba, Alois Panholzer
We study several exactly solvable Polya-Eggenberger urn models with a \emph{diminishing} character, namely, balls of a specified color, say are completely drawn after a finite…
A curious identity in connection with saddle-point method and Stirling's formula
Hsien-Kuei Hwang
We prove the curious identity in the sense of formal power series: \[ \int_{-\infty}^{\infty}[y^m] \exp\left(-\frac{t^2}2 +\sum_{j\ge3}\frac{(it)^j}{j!}\, y^{j-2}\right)\mathrm{d}…
Identities and periodic oscillations of divide-and-conquer recurrences splitting at half
Hsien-Kuei Hwang, Svante Janson, Tsung-Hsi Tsai
We study divide-and-conquer recurrences of the form \begin{equation*} f(n) = αf(\lfloor \tfrac n2\rfloor) + βf(\lceil \tfrac n2\rceil) + g(n) \qquad(n\ge2), \end{equation*} with $g…
Bell numbers in Matsunaga's and Arima's Genjikō combinatorics: Modern perspectives and local limit theorems
Xiaoling Dou, Hsien-Kuei Hwang, Chong-Yi Li
We examine and clarify in detail the contributions of Yoshisuke Matsunaga (1694?--1744) to the computation of Bell numbers in the eighteenth century (in the Edo period), providing…
Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow
Hsien-Kuei Hwang, Emma Yu Jin, Michael J. Schlosser
We establish the asymptotic normality of the dimension of large-size random Fishburn matrices by a complex-analytic approach. The corresponding dual problem of size distribution un…