# Category Archives: Math

## Scoot Over

Each of the two scutoids depicted below contain 2-D examples of my two favorite families of convex polytopes–the permutahedra (the hexagon) and associahedra (the pentagon, also the 2-D stellahedron, OEIS A248727), related to multiplicative (OEIS A133314) and compositional (OEIS A133437) … Continue reading

## Pre-Lie algebras, Cayley’s analytic trees, and mathemagical forests

Referring to week 299 of John Baez’s old blog or the Pre-Lie Algebra entry of nLab, a left pre-Lie algebra satisfies the associative relation, (AR), . To see the relation to Cayley’s work of 1857 as described in my pdf … Continue reading

## Formal group laws and binomial Sheffer sequences

Given a compositional inverse pair and , i.e., , with with , , and , construct the binomial Sheffer sequence with the exponential generating function . Then the associated formal group law (FGL) may be expressed as

## An Intriguing Tapestry: Number triangles, polytopes, Grassmannians, and scattering amplitudes

(This is a duplicate of a Mathoverflow question posed in Oct 2014 that ran the gauntlet of the OCD cadre there–the demonstrative ones I assume avoid stepping on cracks in the sidewalk and become obstructive, hostile, and/or jealous at popular … Continue reading

## Compositional Inverse Operators and Sheffer Sequences

When considering operator inverses, one usually considers multiplicative inverses. As noted earlier in several entries, particularly, “Bernoulli and Blissard meet Stirling … ” (BBS), we see compositional inverse pairs of operators playing an important role in making associations among important … Continue reading