Monthly Archives: November 2016

Witt Differential Generator for Special Jack Symmetric Functions / Polynomials

Exploring some relations among the multinomial coefficients of OEIS A036038 and the compositional inversion formulas of A134264, A248120, and A248927, related to numerous combinatorial structures and areas of analysis, including noncrossing partitions and free probability,  I came across the Jack … Continue reading

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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

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Compositional Inverse Operators and Sheffer Sequences

When considering operator inverses, one usually considers multiplicative inverses. As noted earlier in several entries, particularly, “Bernoulli and Blissard meet Stirling … ” (BBS), we see compositional inverse pairs of operators playing an important role in making associations among important … Continue reading

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The Lagrange Reversion Theorem and the Lagrange Inversion Formula

From Wikipedia on the LRT, with , . Letting and ,  and , giving , the Lagrange inversion formula about the origin, whose expansion in the Taylor series coefficients of is discussed in OEIS A248927. See also A134685. For connections … Continue reading

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