Algebras with two multiplications and their cumulants

@article{Burchardt2018AlgebrasWT,
title={Algebras with two multiplications and their cumulants},
author={Adam Burchardt},
journal={arXiv: Combinatorics},
year={2018}
}

Cumulants are a notion that comes from the classical probability theory, they are an alternative to a notion of moments. We adapt the probabilistic concept of cumulants to the setup of a linear space equipped with two multiplication structures. We present an algebraic formula which involves those two multiplications as a sum of products of cumulants. In our approach, beside cumulants, we make use of standard combinatorial tools as forests and their colourings. We also show that the resulting… Expand