Polynomial Probability Generating Functions with All Roots Real


Di Warren


Research Report 97-32
Date: 26 November 1997


The inherent difficulty in applying the Frobenius-Harper technique (Frobenius, 1910; Harper, 1967) to any setting, is proving that the roots of the polynomial p.g.f. are all real. We give two theorems providing sufficient conditions. This work supplies the technical proofs to Warren (1997).

Key phrases

generating function. real roots.

AMS Subject Classification (1991)

Primary: 60J10
Secondary: 60C05, 60F05, 39A10


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