Shadows of Simplicity

I posted on MathOverflow almost three years ago a question related to characterizing three sets of partition polynomials–the associahedra partition polynomials [A] for compositional inversion / signed refined face partition polynomials / refined Euler cha…

In April I posted on Math StackExchange a reference request for existing literature on a refinement of Kreweras’ relation between the faces of the associahedra and restricted noncrossing partitions of the root system .

In the last few days I have refined a post on MathOverflow that shows the relationship between the geometry of unit hypercubes and the formal power series, or ordinary generating function (o.g.f), that is the reciprocal, or multiplicative inverse, of a fo…

This is a belated transcription of a compilation made in 2023 of the first few multivariate polynomials of the sets of (m)- associahedra and complementary (m)-noncrossing partitons polynomials and and their natural reductions for m=3 to m=-3 discussed in…

I have several hundreds of pages of math notes I need to organize and publish here, but given current events and the plights of so many millions affected by the current callous regime in the U.S., I’m compelled by my conscience to direct people to a poign…

Define the logarithm of the derivative operator, , or more precisely , as the infinitesimal generator (IG) for the fractional integroderivative op of the Heaviside-Pincherle family of the fractional calculus such that, for real, where is the Heaviside step

The Helmut Hasse finite diff rep of Bernoulli number umbral translation, or Bernoulli polynomial umbral substitution, discussed in my previous posts, is most easily seen as an umbral generalization of Newton series translation, a translation expressed in…

The objective of this short pdf is to reveal, via the extended umbral operational calculus of Appell Sheffer polynomial sequences, relationships among the Bernoulli function; its umbral inverse function, the reciprocal function; and the digamma function a…

I added a supplement to one of my old MSE questions “Original author of an exponential generating function for the Bernoulli numbers?

I’ve written over several years on the permutahedra / permutohedra–a family of convex polytopes–and the connections among their geometry, in particular, their associated refined Euler characteristics / refined, signed face polynomials; the algebra of mult…