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 ...

This is a preview. Log in through your library . Abstract Results are obtained which given an upper bound on the number of compact subsets of a topological space in terms of other cardinal invariants.

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 ...

Number theorists are always looking for hidden structure. And when confronted by a numerical pattern that seems unavoidable, they test its mettle, trying hard—and often failing—to devise situations in ...

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 ...