On a set-theoretic invariant
Dion Gijswijt, Pieter Moree
Abstract
Let a1,...,am be positive real numbers. Besser and Moree considered weighted numbers of -1,+1 solutions of the linear inequality |ai-aj| < ekak < ai+aj, with ek=-1 of 1 and k running over the integers 1,...,m with i and j skipped. They introduced some invariants and near invariants related to this situation (invariant meaning here: not depending on the choice of i and j). The main result of their paper is extended here to a much more general setting, namely that of certain maps from finite sets to -1,1. Some applications are given.
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