Author Archives: Tom Copeland

Working Abroad

I’m interested in working abroad in S.E. Asia, including Vietnam and Thailand where some researchers follow my blog, and in Europe or Israel, particularly along the Mediterranean but including Portugal. Please let me know if you feel that my talents … Continue reading

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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.

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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.

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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

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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

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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

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