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Generators, Inversion, and Matrix, Binomial, and Integral Transforms
Generators, Inversion, and Matrix, Binomial, and Integral Transforms is a belated set of notes (pdf) on a derivation of a generating function for the row polynomials of OEISA111999 from its relation to the compositional inversion (a Lagrange inversion formula, LIF) presented … Continue reading →
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Tagged Appell polynomial sequences, Bell polynimials, Binomial Sheffer sequences, BorelLaplace transform, Compositional inverse, Compositional inversion, Cycle index polynomials of symmetric group, Differential operators, Euler binomial transforms, Exponential generating functions, Infinitesimal generators, Lagrange inversion, Lah polynomials, OEIS133437, OEIS134685, OEISA036039, OEISA036040, OEISA111999, OEISA130561, OEISA133932, Ordinary generating function, Reverse polynomials, Series reversion, Sheffer polynomials, Stirling numbers of the first kind, Stirling numbers of the second kind, Upper incomplete gamma function

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The Refined Lives of the F and HVectors of Associahedra
The compositional inversions noted in the Oct. 9th entry “Flipping Functions with Permutohedra” have counterparts with respect to the associahedra, or Stasheff polytopes. The hpolynomials of the simplicial complexes dual to the associahedra (see the Narayana number triangle OEISA001263) can … Continue reading →