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A one-parameter deformation of the Farahat-Higman algebra

Abstract : We show, by introducing an appropriate basis, that a one- parameter family of Hopf algebras introduced by Foissy [L. Foissy, Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations, Adv. Math. 218 (1) (2008) 136-162] interpolates between the Faà di Bruno algebra and the Farahat-Higman algebra. Its structure constants in this basis are deformations of the top connection coefficients, for which we obtain analogues of Macdonald's formulas.
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Jean-Paul Bultel. A one-parameter deformation of the Farahat-Higman algebra. European Journal of Combinatorics, Elsevier, 2011, pp.308-323. ⟨10.1016/j.ejc.2010.10.008⟩. ⟨hal-00825448⟩

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