# Author Archives: Tom Copeland

## 3-D and 2-D Permutohedrons in Nature

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## A Centroid Computation

This is a temporary pedagogical post of an elementary computation of a centroid required in an application to a potential employer.

## A Vector Calculus Computation of the Volume of a Parallelpiped

This is a temporary pedagogical entry of a simple vector triple product calculation required in an application to a potential employer.

## 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