Tom Copeland on Pre-Lie algebras, Cayley… Tom Copeland on Depressed Equations and Genera… Tom Copeland on The Lagrange Reversion Theorem… Tom Copeland on Compositional Inverse Pairs, t… Tom Copeland on Squaring Triangles
Monthly Archives: September 2019
The magic of Mangoldt summoning Riemann’s miraculous miniscules-the nontrivial zeros. In response to observations initiated by Matt McIrvin of a sum of exponentials of the imaginary part of the non-trivial zeroes of the Riemann zeta function, assuming the Riemann hypothesis … Continue reading
Ongoing collection of quotes attributed (mod my lapses in memory) to mathematicians and physicists or about their work: d’Alembert: Go forward, faith will follow!
In the Realm of Shadows: Umbral inverses and associahedra, noncrossing partitions, symmetric polynomials, and similarity transforms
In the earlier post Compositional Inverse Operators and Sheffer Sequences, I constructed relations among a generic power series, call it , or ordinary generating function (o.g.f.), its compositional inverse and four sets of Sheffer polynomial sequences–two Appell sequences and and … Continue reading
This post illustrates what Feynman praised as a beautiful facet of mathematics–abstraction from the concrete–as well as the fascinating synergy at one of its crossroads–that of algebra and enumerative geometry. One day last fall in a class, several curious 12-th … Continue reading
The arXiv “Commutators, matrices and an identity of Copeland” by Darij Grinberg proves and extends an identity I proposed for a matrix computation of the partition polynomials generated by iterated multiplication of a tangent vectorwhere and is a function or … Continue reading