## A characterization of partition polynomials and good Bernoulli trial measures in many symbols

### Volume 135 / 2014

Colloquium Mathematicum 135 (2014), 263-293
MSC: Primary 28A12; Secondary 37A05, 13F20.
DOI: 10.4064/cm135-2-7

#### Abstract

Consider an experiment with $d+1$ possible outcomes, $d$ of which occur with probabilities $x_1,\ldots ,x_d$. If we consider a large number of independent occurrences of this experiment, the probability of any event in the resulting space is a polynomial in $x_1,\ldots ,x_d$. We characterize those polynomials which arise as the probability of such an event. We use this to characterize those $\vec{x}$ for which the measure resulting from an infinite sequence of such trials is good in the sense of Akin.