Difference equations, Combinatorial aspects of partitions of integers, binary partition function, refinement equation, Computer-aided design (modeling of curves and surfaces), Asymptotics; Binary expansion; Binary partition function; Cyclotomic polynomial; Positive matrix; Refinement equation; Subdivision scheme; Algebra and Number Theory; Computational Mathematics; Applied Mathematics, Additive number theory; partitions, asymptotics, positive matrix, Norms of matrices, numerical range, applications of functional analysis to matrix theory, binary expansion, cyclotomic polynomial, subdivision scheme