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# Tag Archives: Eulerian numbers

## 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

## The Elliptic Lie Triad: KdV and Riccati Equations, Infinigens, and Elliptic Genera

The Elliptic Lie Triad: Riccati and KdV Equations, Infinigens, and Elliptic Genera (This site was not correctly updating, so the notes were transcribed to this pdf.) Addendum to The Elliptic Lie Triad

Posted in Math, Uncategorized
Tagged Bernoulli numbers, Burgers' equation, Chebyshev polynomials, Combinatorics, Compositional inverse, Differential operators, Elliptic curves, Elliptic formal group law, Elliptic genera, Enumerative combinatorics, Euler numbers, Eulerian numbers, Evolution equations, Faber polynomials, Geodesics of Virasoro-Bott group, Grassmann polynomials, Grassmannian, Heat equation, Hyperbolic tangent, Infinigens, Infinitesimal generators, KdV, Korteweg-de Vries equation, L-genus, Lie algebra, Lucas (Cardan) polynomials, Refined Eulerian numbers, Riccati, Schwarzian derivative, SL2, Solitons, Swiss knife polynomials, Viscous Burgers equation
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## Appell polynomials, cumulants, noncrossing partitions, Dyck lattice paths, and inversion

The raising op for any Appell sequence is determined by the derivative of the log of the e.g.f. of the basic number sequence, connecting the op to the combinatorics of the cumulant expansion OEIS-127671 of the moment generating function and … Continue reading

Posted in Math
Tagged Appell sequences, Associahedra, Bernoulli, Bernoulli polynomials, Catalan numbers, Compositional inverse, Cumulants, Dyck lattce paths, Eulerian numbers, Free cumulants, Free probability, Hirzebruch Todd class criterion, Lagrange inversion, Noncrossing partitions, Permutohedra, Raising operators, Riemann zeta
2 Comments

## Flipping Functions with Permutohedra

Flipping Functions with Permutohedra : A short note on forming the multiplicative and compositional inverses of functions using the refined Eulerian h-polynomials OEIS-A145271 and refined face polynomials of permutohedra OEIS-A049019.

## Mathemagical Forests

The set of notes Mathemagical Forests is an expansion of the May notes and discusses some connections between rooted trees, derivative operators, Lagrange inversion, the Legendre transformation, the Faa di Bruno formula, Sheffer sequences and umbral calculus, and the infinite dimensional Witt … Continue reading

Posted in Math
Tagged Cayley, Comtet, Connes-Muscovi, Creation and annihilation operators, Eulerian numbers, Faa di Bruno formula, integer arrays, Iterated derivatives, Lagrange inversion, Legendre transformation, Lie Witt algebra, Number triangles, Operator ordering, Raising and lowering operators, Rooted trees, Sheffer sequences, triangular matrices, Umbral calculus
3 Comments