Zobrazeno 1 - 10
of 931
pro vyhledávání: '"Foissy A."'
Higher-order notions of Kreweras complementation have appeared in the literature in the works of Krawczyk, Speicher, Mastnak, Nica, Arizmendi, Vargas, and others. While the theory has been developed primarily for specific applications in free probabi
Externí odkaz:
http://arxiv.org/abs/2407.17660
Autor:
Foissy, Loïc
We study the compatibility between the antipode and the preLie product of a Com-PreLie Hopf algebra, that is to say a commutative Hopf algebra with a complementary preLie product, compatible with the product and the coproduct in a certain sense. An e
Externí odkaz:
http://arxiv.org/abs/2406.01120
Autor:
Foissy, Loïc, Malvenuto, Claudia
We compute an explicit formula for the antipode of the double bialgebra of graphs in terms of totally acyclic partial orientations, using some general results on double bialgebras. In analogy to what was already proven in Hopf-algebraic terms for the
Externí odkaz:
http://arxiv.org/abs/2404.05497
Autor:
Foissy, Loïc, Patras, Frédéric
We here construct an explicit isomorphism between any commutative Hopf algebra which underlying coalgebra is the tensor coalgebra of a space $V$ and the shuffle algebra based on the same space. This isomorphism uses the commutative $B_\infty$ structu
Externí odkaz:
http://arxiv.org/abs/2401.13317
Autor:
Foissy, Loïc
We prove that the Lie algebra of primitive elements of a graded and connected bialgebra, free as an associative algebra, over a eld of characteristic zero, is a free Lie algebra. The main tool is a ltration, which allows to embed the associated grade
Externí odkaz:
http://arxiv.org/abs/2309.16199
Publikováno v:
European Journal of Combinatorics, Volume 120, 2024, 103967
We show that the chronological removal of cycles from a walk on a graph, known as Lawler's loop-erasing procedure, generates a preLie co-algebra on the vector space spanned by the walks. In addition, we prove that the tensor and symmetric algebras of
Externí odkaz:
http://arxiv.org/abs/2306.17605
Autor:
Foissy, Loïc
Using the formalism of species and twisted objects, we introduce two structures of cointeracting bialgebras on hypergraphs, induced by two notions of induced sub-hypergraphs. We study the associated unique morphisms of cointeracting bialgebras from h
Externí odkaz:
http://arxiv.org/abs/2304.00810
Autor:
Foissy, Loïc
We introduce two coproducts on mixed graphs (that is to say graphs with both oriented and unoriented edges), the first one by separation of the vertices into two parts, and the second one given by contraction and extractions of subgraphs. We show tha
Externí odkaz:
http://arxiv.org/abs/2301.09449
Autor:
Foissy, Loïc
We introduce a notion of extraction-contraction coproduct on twisted bialgebras, that is to say bialgebras in the category of linear species. If $P$ is a twisted bialgebra, a contraction-extraction coproduct sends $P[X]$ to $P[X/\sim]\otimes P[X]$ fo
Externí odkaz:
http://arxiv.org/abs/2301.09447
We define a notion of higher order renormalization group equation and investigate when a sequence of trees satisfies such an equation. In the strongest sense, the sequence of trees satisfies a $k$th order renormalization group equation when applying
Externí odkaz:
http://arxiv.org/abs/2209.06576