Tag Archives: Stirling partition polynomials of the second kind
(m)-Associahedra and (-m)-Noncrossing Partition Polynomials as Moments of Umbral Inverse Appell Polynomial Sequences
Numerous relations between the pair of sets of (m)-associahedra and (-m)-noncrossing partitions / (-m)-Narayana partition polynomials can be deduced from treating them as the moments of an umbral inverse pair of Appell-Sheffer polynomials sequences. (m)-Associahedra and (-m)-Noncrossing Partition Polynomials as … Continue reading
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Tagged (m)-associahedra partition polynomials, (m)-Narayana partition polynomials, (m)-noncrossing partitions polynomials, complete homogeneous symmetric polynomials, Composition partition polynomials, Compositional inverse, Cycle index polynomials of the symmetric groups, Differential operators, elementary symmetric polynomials, Faber polynomials, Facc di Bruno / Bell partition polynomials, Group theory, Inverse matrices, Ladder operators, Lah partition polynomia;s, logarithmic derivative, lowering operator, Matrix representations, Multiplicative inverse, Permutahedra, Permutation matrix, Power sum symmetric polynomials, Raising operator, reciprocals, Recursion, Riordan production matrix, Sheffer sequences, Stirling partition polynomials of the second kind, Stirling patition polynomials of the fist kind, Striling partition polynomials of the second kind, Symmetric function theory, Symmetric polynomials, triangular matrices, Umbral compostional inverse, Umbral inverse pairs
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Stirling Raisings
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
Posted in Math
Tagged Appell sequences, Bell polynomials, compositional partition polynomials, Creation operator, Differential operators, Faa di Bruno partition polynomials, Ladder operators, Polynomial sequences, Raising operator, Stirling partition polynomials of the second kind, Umbral calculus
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