On an invariant related to a linear inequality
Abstract
Let A be an m-dimensional vector with positive real entries. Let Ai,j be the vector obtained from A on deleting the entries Ai and Aj. We investigate some invariant and near invariants related to the solutions E (m-2 dimensional vectors with entries either +1 or -1) of the linear inequality |Ai-Aj| < <E,Ai,J> < Ai+Aj, where <,> denotes the usual inner product. One of our methods relates, by the use of Rademacher functions, integrals involving trigonometric quantities to these quantities.
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