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Birth Processes and Symmetric Polynomials
T. Bickel, N. Galli, and K. Simon
Institute for Theoretical Computer Science, ETH zentrum, 8092 Zurich, Switzerland
{bickel, galli, simon}@inf.ethz.ch
Annals of Combinatorics 5(2) p.123-139 June, 2001
AMS Subject Classification: 05A30, 05A19, 60J10, 11B65
Abstract:
Many discrete-time pure birth processes are symmetrical in the following sense: The probability that the process is in a fixed state is independent of the sequence of transitions inducing . This is always the case whenever a transition is a time-dependent or a state-dependent random variable or the product of such independent variables. We use this property in order to derive algebraic descriptions in terms of symmetric polynomials. Besides new solutions, our approach offers a uniform point of view on a large class of often considered distributions.
Keywords: generalized Stirling numbers, birth processes, symmetric polynomials

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