Decomposition and enumeration in partially ordered sets

The method of preventing color-degrading interactions between certain optical brighteners and filaments made from a modacrylic polymer containing as a copolymer a halogenated ethylenically unsaturated monomer, the optical brightener preferably having the formula: where X and Y are basic groups selected from the group consisting of -NH2, -H(CH3)2, and -N+(CH3)3Z, where Z is selected from the group consisting of chloride, sulphate and bromide anions, n is 0 to 3, and R is an alkyl group containing 1 to 4 carbon atoms, wherein an aqueous liquid is applied to the filaments, the liquid containing 0.01 to 0.5 weight percent of a compound having the formula: wherein R is a member selected from the group consisting of an alkyl radical having 1 to 11 carbon atoms, a phenyl radical and an alkyl phenyl radical containing no more than eight carbon atoms.