Author Archives: Tom Copeland

3-D and 2-D Permutohedrons in Nature

Advertisements

Posted in Math | Tagged , | Leave a comment

A Centroid Computation

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

Posted in Uncategorized | Leave a comment

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.

Posted in Uncategorized | Leave a comment

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

Posted in Math | Tagged , , , , | Leave a comment

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

Posted in Math | Tagged , , , , , , , , , | Leave a comment

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

Posted in Math | Tagged , , , , , , , , , , , , , | 1 Comment

An lnfinite Wronskian Matrix, Binomial Sheffer Polynomials, and the Lagrange Reversion Theorem

Form the infinite Wronskian matrix with elements . A generating function for this matrix is with . If , then also , where is a binomial Sheffer sequence of polynomials. Then in this particular case, and so is the product … Continue reading

Posted in Math | Tagged , , , , , , , , | Leave a comment