Algebras with two multiplications and their cumulants
@article{Burchardt2019AlgebrasWT, title={Algebras with two multiplications and their cumulants}, author={Adam Burchardt}, journal={Journal of Algebraic Combinatorics}, year={2019} }
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…
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