2 problems

Let $R_t(w)=\sum_{n=1}^{\infty}tnw^n=\frac{tw}{(1-w)^2}$, and let $F^{\boxplus t}$ denote the corresponding free-power transform. The value $t=27/8$ yields a probability distributi…

Let $cgamma=-\delta$, and let $cR_2,cR_3,cdots$ denote the free cumulants, viewed as functions on Young diagrams. For each partition $cpi$, the Jack character…