Tag Archives: Free moments
Interpretations of the (−m)−Fuss-Narayana numbers for m>0
In much of the literature, these are called the positive Catalan numbers with ‘positive’ based on geometric considerations. My terminology is based on a broader, more algebraic perspective. I posed a question about interpretations on MathOverflow presenting many I know … Continue reading
Posted in Math
Tagged (m)-associahedra partition polynomials, (m)-Narayana partition polynomials, (m)-noncrossing partitions polynomials, Combinatorial reciprocity, coral diagrams, Dyck paths, flag simplicial complexes, Free cumulants, Free moments, Free probability theory, Fuss-Catalan numvers, Fuss-Narayana numbers, generalized cluster complexes, inverse Narayana polynomials, Inverse noncrossing partition polynomials, positive Catalan numbers, probability distributions, Raney distributions, Raney numbers, Trees, Weyl-Coxeter group A_n
1 Comment
A Taste of Moonshine in Free Moments
The pdf below presents relations among compositional and multiplicative inversions, Laurent series, and the formal free cumulants and moments of free probability. One example is the q-expansion of Klein’s j-invariant found in monster moonshine. Another is based on Motzkin numbers. … Continue reading
Shadows of Simplicity 