4 papers
Diophantine Equations of Matching Games I
Chun Yin Hui, Wai Yan Pong
We solve a family of quadratic Diophantine equations associated to a simple kind of games. We show that the ternary case, in many ways, is the most interesting and the least arbitr…
Length Spectra of Natural Numbers
Wai Yan Pong
Two numbers are spectral equivalent if they have the same length spectrum. We show how to compute the equivalence classes of this relation. Moreover, we show that these classes can…
Sums of Consecutive Integers
Wai Yan Pong
A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural num…
Orderings of Monomial Ideals
Matthias Aschenbrenner, Wai-Yan Pong
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of…