## Marcelo Aguiar ; Aaron Lauve - Lagrange's Theorem for Hopf Monoids in Species

dmtcs:2887 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2887
Lagrange's Theorem for Hopf Monoids in Species

Authors: Marcelo Aguiar ; Aaron Lauve

We prove Lagrange's theorem for Hopf monoids in the category of connected species. We deduce necessary conditions for a given subspecies $\textrm{k}$ of a Hopf monoid $\textrm{h}$ to be a Hopf submonoid: each of the generating series of $\textrm{k}$ must divide the corresponding generating series of $\textrm{k}$ in ℕ〚x〛. Among other corollaries we obtain necessary inequalities for a sequence of nonnegative integers to be the sequence of dimensions of a Hopf monoid. In the set-theoretic case the inequalities are linear and demand the non negativity of the binomial transform of the sequence.

Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: Hopf monoids,species,graded Hopf algebras,Lagrange's theorem,generating series,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Fundings :
Source : OpenAIRE Research Graph
• Categories, Hopf Algebras, and Algebraic Combinatorics; Funder: National Science Foundation; Code: 1001935

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