Tag Archives: Faa di Bruno partition polynomials

Stirling Raisings

Posted on February 10, 2022 by Tom Copeland

The pdf below presents three creation / raising ops for an avatar of the refined Stirling partition polynomials of the second kind (OEIS A036040), also associated with Scherk, Touchard, and Steffensen, but most commonly linked to Bell and Faa di … Continue reading →

Calculus, Combinatorics, and Geometry Underlying OEIS A060540, and the Exponential Formula

Posted on June 12, 2021 by Tom Copeland

The pdf below gives the associations of OEIS A060540 with the operator calculus of Appell Sheffer polynomials, the combinatorics of simple set partitions encoded in the Faa di Bruno formula for composition of analytic functions (formal Taylor series), and the … Continue reading →

Posted in Math | Tagged Appell raising operators, Appell Sheffer polynomial sequences, compositional partition polynomials, Differential operators, Exponential formula, Faa di Bruno partition polynomials, hypertetrahedra, hypertriangles, n-simplices, OEIS 036040, OEIS A060540, Set partitions | 3 Comments

Road map to OEIS sequences related to symmetric functions / polynomials and basic analysis

Posted on June 4, 2021 by Tom Copeland

A short list of OEIS sequences related to polytopes, multiplicative and compositional inversion of power series, composition, and transformations among symmetric functions. The arrows indicate refinement of a sequence. The multiplicative and compositional inversions are graded, so can, for example, be … Continue reading →

Posted in Math | Tagged Associahedra, Bell, Bell polynomials, Catalan, Chebyshev Hermite polynomials, Classical cumulants and moments, complete homogeneous symmetric polynomials, Composition, Compositional inversion, Cycle index polynomials of the symmetric groups, Differential operators, double factorial, Elementary Schur polynomials, elementary symmetric polynomials, Eulerian numbers, Exponential generating functions, Faa di Bruno partition polynomials, Faber partition polynomials, face numbers, free cumulants and moments, Lah, Lah polynomials, Laurent serie, Laurent series, Lie infinitesimal generators, Logarithmic polynomials, Matrix representation of derivative operators, Moebius transformation, multiplicative inversion, Narayana numbers, Newton identities, normal ordering, OEIS, Ordinary generating functions, Pascal triangle, Perfect matchings, Permutohedra, Pontryagin partition polynomials, Power series, power sum polynomials, Reciprocal, Refined Euler characteristic polynomial, Refined Eulerian numbers, refined Lah polynomials, Schroeder numbers, Schur self-convolution expansion coefficients, Simplices, Stirling numbers of the first kind, Stirling numbers of the second kind, symmetric functions, Ward polynomials, Witt algebra | 4 Comments

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Tag Archives: Faa di Bruno partition polynomials

Stirling Raisings

Calculus, Combinatorics, and Geometry Underlying OEIS A060540, and the Exponential Formula

Road map to OEIS sequences related to symmetric functions / polynomials and basic analysis

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