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- W3100102895 abstract "Abstract Following Radford's proof of Lagrange's theorem for pointed Hopf algebras, we prove Lagrange‘s theorem for Hopf monoids in the category of connected species. As a corollary, we obtain necessary conditions for a given subspecies k of a Hopf monoid h to be a Hopf submonoid: the quotient of any one of the generating series of h by the corresponding generating series of k must have nonnegative coefficients. Other corollaries include a necessary condition for a sequence of nonnegative integers to be the dimension sequence of a Hopfmonoid in the formof certain polynomial inequalities and of a set-theoretic Hopf monoid in the form of certain linear inequalities. The latter express that the binomial transform of the sequence must be nonnegative." @default.
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- W3100102895 date "2013-04-01" @default.
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- W3100102895 title "Lagrange's Theorem for Hopf Monoids in Species" @default.
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- W3100102895 doi "https://doi.org/10.4153/cjm-2011-098-9" @default.
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