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- W2404506570 abstract "To any poset or quasi-poset is attached a lattice polytope, whose Ehrhart polynomial we study from a Hopf-algebraic point of view. We use for this two interacting bialgebras on quasi-posets. The Ehrhart polynomial defines a Hopf algebra morphism taking its values in Q[X], we deduce from the interacting bialgebras an algebraic proof of the duality principle, a generalization and a new proof of a result on B-series due to Whright and Zhao, using a monoid of characters on quasi-posets, and a generalization of Faulhaber's formula. We also give non-commutative versions of these results: polynomials are replaced by packed words. We obtain in particular a non-commutative duality principle." @default.
- W2404506570 created "2016-06-24" @default.
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- W2404506570 date "2019-01-01" @default.
- W2404506570 modified "2023-09-25" @default.
- W2404506570 title "Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials" @default.
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