Monthly Archives: July 2023
(m)-Associahedra and (m)-Noncrossing Partition Polynomials and the Infinite Dihedral Group
I was playing around once again yesterday with the basic algebraic relations among the sets of (m)-associahedra partition polynomials and the sets of (m)-noncrossing partitions polynomials , which I’ve presented in several posts over the last year or so, and … Continue reading
Iterative formula for the Kreweras-Voiculescu polynomials–the noncrossing partitions polynomials
The Kreweras-Voiculescu partition polynomials, which I usually call the noncrossing partitions or the refined Narayana partition polynomials of OEIS A134264–flag and enumerate distinct noncrossing partitions and give the free moments in terms of the free cumulants in free probability theory. … Continue reading
Noncrossing partitions and (-1)-associahedra partition polynomials as Appell and quasi-Appell sequences
The following pdf concerns the celebrated partition polynomials of OEIS A134264 for compositional inversion of power series / ordinary generating functions (core partition polynomials in free probability theory, related to the combinatorics of Dyck paths, noncrossing partitions, parking functions, and … Continue reading
The umbral compositional inverse of a Sheffer polynomial sequence and its lowering and raising operators
The pdf The umbral compositional inverse of a Sheffer polynomial sequence and its lowering and raising operators reprises results of older notes. See the MO-Q “Grothendieck schemes and the Sheffer differential op calculus (Rota, Roman, et al. finite operator calculus)” … Continue reading
Shadows of Simplicity 