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# Tag Archives: Associahedra

## 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

## A Class of Differential Operators and the Stirling Numbers

The differential operator with can easily be expanded in terms of the operators by considering its action on

Posted in Math
Tagged Associahedra, Bell polynomials, Differential operators, Falling factorials, Generalized Dobinski relation, Generalized Stirling numbers, Lah polynomials, Lie derivatives, Moebius transformation, Rising factorials, SL2 group, Stirling numbers of the first kind, Stirling numbers of the second kind, Umbral calculus, Umbral inverse pair, Witt-Lie algebra
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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
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## Compositional Inverse Pairs, the Inviscid Burgers-Hopf Equation, and the Stasheff Associahedra

Compositional Inverse Pairs, the Inviscid Burgers-Hopf Equation, and the Stasheff Associahedra: A brief note (pdf) on some relations among these topics, including the Catalan and Fuss-Catalan numbers. References are provided linking the analysis with the distribution of eigenvalues of random … Continue reading