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Cointeracting Bialgebras

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No logo availableInstitut des Hautes Études Scientifiques (IHÉS)
 Foissy, Loïc

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Cointeracting Bialgebras
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28
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CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Pairs of cointeracting bialgebras recently appears in the literature of combinatorial Hopf algebras, with examples based on formal series, on trees (Calaque, Ebrahimi-Fard, Manchon), graphs (Manchon), posets... We will give several results obtained on pairs of cointeracting bialgebras: actions on the group of characters, antipode, morphisms to quasi-symmetric functions... and we will give applications to Ehrhart poylnomials and chromatic polynomials.