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Symmetric GroupAlgebraic CombinatoricsRepresentation TheorySymmetric FunctionCluster AlgebraHecke AlgebraStandard Young TableauxGenerating FunctionSchur FunctionPolynomialLower BoundHyperplane ArrangementHopf AlgebraTensor ProductCombinatorial FormulasSet PartitionsExplicit FormulaAffine Hecke AlgebrasSchur PolynomialPositive Integer