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# Tag Archives: Free probability

## Commutators, matrices and an identity of Copeland

The arXiv “Commutators, matrices and an identity of Copeland” by Darij Grinberg proves and extends an identity I proposed for a matrix computation of the partition polynomials generated by iterated multiplication of a tangent vectorwhere and is a function or … Continue reading

Posted in Math
Tagged algebraic combinatorics, Algebraic geometry, Appell polynomial sequences, Associahedra, Butcher series, Combinatorics, commutators, Compositional inversion, convex polytopes, Dyck paths, enumerative geometry, Evolution equations, free cumulants and moments, Free probability, generalized permutahedra, Hirzebruch criterion, Hopf algebra of monoids, inviscid Burgers' equation, iterated convolutions, Kdv equation, Koszul duality, matices, Noncrossing partitions, phylogenetic trees, polygon dissections, Pre-Lie algebra, rooted Cayley trees, Todd class
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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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