2016/05/26 by Loïc Foissy, Foissy, Loïc · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1605.08310
openalex publication_date 2016/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.