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Probability and the elementary symmetric functions

Published online by Cambridge University Press:  24 October 2008

J. Denmead Smith
J. Denmead Smith
Affiliation:
College of the Resurrection, Mirfield, Yorkshire
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Extract

Let p be a prime, and suppose that x1,…,xN are independent random variables which take the values 0, 1,…,p − 1 with probabilities s0, sl…,sp−1 where s0+…+sp−1 = 1 and 0 < sk < 1 for each k. PN(n) denotes the probability that the elementary symmetric function σr(x1,…,xN) = ∑x1…,xr of the rth degree in the variables x1,…,xN is congruent, modulo p, to a prescribed integer n.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 133 - 139
Copyright
Copyright © Cambridge Philosophical Society 1973

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