12 citations · 76 across the 61 of their papers we have counts for
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A theory of pictures for quasi-posets
Loïc Foissy, Claudia Malvenuto, Frédéric Patras
The theory of pictures between posets is known to encode much of the combinatorics of symmetric group representations and related topics such as Young diagrams and tableaux. Many r…
Chromatic polynomials and bialgebras of graphs
Loïc Foissy
The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures: the first coproduct is given by parti…
Lie theory for quasi-shuffle bialgebras
Loïc Foissy, Frédéric Patras
Many features of classical Lie theory generalize to the broader context of algebras over Hopf operads. However, this idea remains largely to be developed systematically. Quasi-shuf…
Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials
Loïc Foissy
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 qua…
Operads of finite posets
Frédéric Fauvet, Loïc Foissy, Dominique Manchon
We describe four natural operad structures on the vector space generated by isomorphism classes of finite posets. The three last ones are set-theoretical and can be seen as a simpl…