ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Abstract. Let a = (a 1,a 2, ¼, a m) Î R>0m. Let a i,j be the vector obtained from a by deleting the entries a i and aj. Besser and Moree introduced some invariants and near invariants related to the solutions e Î{±1}m-2 of the linear inequality |ai - aj| < <e,ai,j> < ai + aj, where < , > denotes the usual inner product and ai,j the vector obtained from a by deleting ai and aj. The main result of Besser and Moree is extended here to a much more general setting, namely that of certain maps from finite sets to {-1,1}.