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Article Dans Une Revue International Journal of Algebra and Computation Année : 2014

Noncommutative Bell polynomials, quasideterminants and incidence Hopf algebras

Résumé

Bell polynomials appear in several combinatorial constructions throughout mathematics. Perhaps most naturally in the combinatorics of set partitions, but also when studying compositions of diffeomorphisms on vector spaces and manifolds, and in the study of cumulants and moments in probability theory. We construct commutative and noncommutative Bell polynomials and explain how they give rise to Fa\`a di Bruno Hopf algebras. We use the language of incidence Hopf algebras, and along the way provide a new description of antipodes in noncommutative incidence Hopf algebras, involving quasideterminants. We also discuss M\"obius inversion in certain Hopf algebras built from Bell polynomials.

Dates et versions

hal-03044362 , version 1 (07-12-2020)

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Kurusch Ebrahimi-Fard, Alexander Lundervold, Dominique Manchon. Noncommutative Bell polynomials, quasideterminants and incidence Hopf algebras. International Journal of Algebra and Computation, 2014, 24 (05), pp.671-705. ⟨10.1142/S0218196714500283⟩. ⟨hal-03044362⟩
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