Relations between cumulants in noncommutative probability
  We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determine the coefficients of these formulas with the exception of the formula for classical cumulants in terms of monotone cumulants whose coefficients are only partially computed. 
Octavio Arizmendi, Takahiro Hasebe, Franz Lehner, Carlos Vargas
math.CO math.OA