4 citations · 13 across the 15 of their papers we have counts for
16 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…
On rearrangement inequalities for T-norm logics
Chai Wah Wu
The rearrangement inequality states that the sum of products of permutations of 2 sequences of real numbers are maximized when the terms are similarly ordered and minimized when th…
Dither computing: a hybrid deterministic-stochastic computing framework
Chai Wah Wu
Stochastic computing has a long history as an alternative method of performing arithmetic on a computer. While it can be considered an unbiased estimator of real numbers, it has a…
On rearrangement inequalities for multiple sequences
Chai Wah Wu
The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the la…
Sums of products of binomial coefficients mod 2 and run length transforms of sequences
Chai Wah Wu
We study properties of functions of binomial coefficients mod 2 and derive a set of recurrence relations for sums of products of binomial coefficients mod 2. We show that they resu…
Minimal number of points on a grid forming line segments of equal length
Chai Wah Wu
We consider the minimal number of points on a regular grid on the plane that generates line segments of points of exactly length . We illustrate how this is related to the $…
Counting the number of isosceles triangles in rectangular regular grids
Chai Wah Wu
In general graph theory, the only relationship between vertices are expressed via the edges. When the vertices are embedded in an Euclidean space, the geometric relationships betwe…
Meertens number and its variations
Chai Wah Wu
In 1998, Bird introduced Meertens numbers as numbers that are invariant under a map similar to the Godel encoding. In base 10, the only known Meertens number is 81312000. We look a…
Permutations such that is maximized or minimized
Chai Wah Wu
We consider the problem of finding the set of permutations of such that is maximized or minimized. While the set of per…
On a conjecture regarding primality of numbers constructed from prepending and appending identical digits
Chai Wah Wu
Consider the operation of adding the same number of identical digits to the left and to the right of a number n. In OEIS sequence A090287, it was conjectured that this operation wi…
On some properties of contracting matrices
Chai Wah Wu
The concepts of paracontracting, pseudocontracting and nonexpanding operators have been shown to be useful in proving convergence of asynchronous or parallel iteration algorithms.…