Journal of Combinatorial Theory Series A
| Hi-index | 0.00 |
We show, by introducing an appropriate basis, that a one-parameter family of Hopf algebras introduced by Foissy [L. Foissy, Faa 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 Faa 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.