Abstract
The Schur–Szegö composition of two polynomials of degree ⩽ n introduces an interesting semigroup structure on polynomial spaces and is one of the basic tools in the analytic theory of polynomials. In the present Note we show how it interacts with the stratification of polynomials according to the multiplicities of their zeros and we present the induced semigroup structure on the set of all ordered partitions of n. To cite this article: V. Kostov, B. Shapiro, C. R. Acad. Sci. Paris, Ser. I 343 (2006).
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