2 citations · 4 across the 10 of their papers we have counts for
13 papers
Generalised flip order on the faces of nestohedra
Pierre-Louis Curien, Bérénice Delcroix-Oger, Jovana Obradović
Classical shuffle products on permutations and binary planar rooted trees (i.e., on the vertices of permutohedra and associahedra) admit descriptions in terms of intervals in the w…
Tridendriform algebras on hypergraph polytopes, the other way around
Pierre-Louis Curien, Bérénice Delcroix-Oger, Jovana Obradović
Hypergraph polytopes (or nestohedra) form a broad class of polytopes obtained by truncating faces of a simplex according to a hypergraph. In earlier work, the authors constructed q…
Lie-operads and operadic modules from poset cohomology
Bérénice Delcroix-Oger, Clément Dupont
As observed by Joyal, the cohomology groups of the partition posets are naturally identified with the components of the operad encoding Lie algebras. This connection was explained…
Cellular diagonals of permutahedra
Bérénice Delcroix-Oger, Guillaume Laplante-Anfossi, Vincent Pilaud +1
We provide a systematic enumerative and combinatorial study of geometric cellular diagonals on the permutahedra. In the first part of the paper, we study the combinatorics of certa…
Tridendriform algebras on hypergraph polytopes
Pierre-Louis Curien, Bérénice Delcroix-Oger, Jovana Obradović
We extend the works of Loday-Ronco and Burgunder-Ronco on the tridendriform decomposition of the shuffle product on the faces of associahedra and permutohedra, to other families of…
Some properties of the parking function poset
Bérénice Delcroix-Oger, Matthieu Josuat-Vergès, Lucas Randazzo
In 1980, Edelman defined a poset on objects called the noncrossing 2-partitions. They are closely related with noncrossing partitions and parking functions. To some extent, his def…
Non-ambiguous trees: new results and generalisation (Full version)
Bérénice Delcroix-Oger, Florent Hivert, Patxi Laborde-Zubieta +2
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yields…
Operads with compatible CL-shellable partition posets admit a Poincaré-Birkhoff-Witt basis
Joan Bellier-Millès, Bérénice Delcroix-Oger, Eric Hoffbeck
In 2007, Vallette built a bridge across posets and operads by proving that an operad is Koszul if and only if the associated partition posets are Cohen-Macaulay. Both notions of be…
An operad is never free as a pre-Lie algebra
Emily Burgunder, Bérénice Delcroix-Oger, Dominique Manchon
An operad is naturally endowed with a pre-Lie structure. We prove that as a pre-Lie algebra an operad is not free. The proof holds on defining a non-vanishing linear operation in t…
Confluence laws and Hopf-Borel type theorem for operads
Emily Burgunder, Bérénice Delcroix-Oger
In 2008, Loday shed light on the existence of Hopf-Boreltheorems for operads. Using the vocabulary of category theory, Livernet,Mesablishvili and Wisbauer extended such theorems to…
Non-ambiguous trees: new results and generalisation
Jean-Christophe Aval, Adrien Boussicault, Berenice Delcroix-Oger +2
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yield…
Semi-pointed partition posets and Species
Bérénice Delcroix-Oger
We define semi-pointed partition posets, which are a generalisation of partition posets and show that they are Cohen-Macaulay. We then use multichains to compute the dimension and…
Decorated hypertrees
Bérénice Oger
C. Jensen, J. McCammond and J. Meier have used weighted hypertrees to compute the Euler characteristic of a subgroup of the automorphism group of a free product. Weighted hypertree…