The following dichotomy is established for any pair F, G of hereditary families of finite subsets of N: Given N, an infinite subset of N, there exists M an infinite subset of N so that either ...

Simple mathematical concepts such as counting appear to be firmly anchored in the natural process of thinking. Studies have shown that even very young children and animals possess such skills to a ...

The subset-sum problem is one of the most frequently occurring NP (nondeterministic, polynomial-time)-complete) problems. It asks whether a subset of numbers in a set of positive integers adds up ...

A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of fractions. Number theorists are always looking for hidden structure. And ...