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}
}
  • Adam Burchardt
  • Published 25 March 2018
  • Mathematics
  • Journal of Algebraic Combinatorics
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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