6 papers
Computing the Greatest Common Divisor of Binomial Coefficients
Chai Wah Wu
The greatest common divisor (GCD) of for is known to be some power of 2 times the product of all odd primes p such that . We complete the a…
On Mixed-Precision Iterative Methods and Analysis for Nearly Completely Decomposable Markov Processes
Vasileios Kalantzis, Mark S. Squillante, Chai Wah Wu
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory o…
Diagrams of opposition: an algebraic viewpoint
Chai Wah Wu
We study the square of opposition and its various geometric generalizations from an algebraic viewpoint. In particular, we show how the various shapes of oppositions can be framed…
Pandigital and penholodigital numbers
Chai Wah Wu
Pandigital and penholodigital numbers are numbers that contain every digit or nonzero digit respectively. We study properties of pandigital or penholodigital numbers that are also…
Faulhaber's formula, Bernoulli numbers, power sums of natural numbers and totatives and the functional equation
Chai Wah Wu
In modern usage the Bernoulli numbers and Bernoulli polynomials follow Euler's approach and are defined using generating functions. Originally, they were derived by Bernoulli while…
Big Two and n-card poker probabilities
Brian Wu, Chai Wah Wu
Between the poker hands of straight, flush, and full house, which hand is more common? In standard 5-card poker, the order from most common to least common is straight, flush, full…