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math.CO2026
The planar Hopf algebra of noncommutative multi-indices
Yong Yu, Xing Gao, Dominique Manchon
We construct the planar Linares--Otto--Tempelmayr Hopf algebra, thereby filling the missing planar noncommutative multi-index corner in the square relating the LOT, Butcher--Connes…
math.CO2024
Submodular functions, generalized permutahedra, conforming preorders, and cointeracting bialgebras
Gunnar Fløystad, Dominique Manchon
Submodular functions defined on the power set of a finite set are in bijection with generalized permutahedra $\egp(z)$. To any such we define a class of preorders, {\it con…
math.CO2024
Free Novikov algebras and the Hopf algebra of decorated multi-indices
Zhicheng Zhu, Xing Gao, Dominique Manchon
We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices that recently appeared in the literature, which can be briefly described as the gr…