%0 Journal Article %1 krawczyk1999combinatorics %A Krawczyk, Bernadette %A Speicher, Roland %D 1999 %K combinatorics probability theory %T Combinatorics of free cumulants %U http://arxiv.org/abs/math/9905094 %X We derive a formula for expressing free cumulants whose entries are products of random variables in terms of the lattice structure of non-crossing partitions. We show the usefulness of that result by giving direct and conceptually simple proofs for a lot of results about $R$-diagonal elements. Our investigations do not assume the trace property for the considered linear functionals.

@article{krawczyk1999combinatorics, abstract = {We derive a formula for expressing free cumulants whose entries are products of random variables in terms of the lattice structure of non-crossing partitions. We show the usefulness of that result by giving direct and conceptually simple proofs for a lot of results about $R$-diagonal elements. Our investigations do not assume the trace property for the considered linear functionals.}, added-at = {2020-02-06T15:19:57.000+0100}, author = {Krawczyk, Bernadette and Speicher, Roland}, biburl = {https://www.bibsonomy.org/bibtex/2cf2aecaa50d0b1ae39f711e6de96b9ad/kirk86}, description = {[math/9905094] Combinatorics of free cumulants}, interhash = {1d8c62696b7fb26d338441262d424c70}, intrahash = {cf2aecaa50d0b1ae39f711e6de96b9ad}, keywords = {combinatorics probability theory}, note = {cite arxiv:math/9905094Comment: 26 pages, Latex2e}, timestamp = {2020-02-06T15:20:36.000+0100}, title = {Combinatorics of free cumulants}, url = {http://arxiv.org/abs/math/9905094}, year = 1999 }