From the 1 of 9 linked papers with an AI index.
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A Hopf algebra on permutations with a coupling product
Huilan Li, Yishuo Yang, Nantel Bergeron
We define a coupling product and a draw coproduct on permutations and show that they define a graded, connected, cocommutative, free Hopf algebra . In characteristic z…
Interval hypergraphic lattices
Nantel Bergeron, Vincent Pilaud
For a hypergraph on , the hypergraphic poset is the transitive closure of the oriented skeleton of the hypergraphic polytope …
Equivariant quasisymmetry and noncrossing partitions
Nantel Bergeron, Lucas Gagnon, Philippe Nadeau +2
We introduce a definition of ``equivariant quasisymmetry'' for polynomials in two sets of variables. Using this definition we define quasisymmetric generalizations of the theory of…
Lattices of acyclic pipe dreams
Nantel Bergeron, Noémie Cartier, Cesar Ceballos +1
We show that for any permutation , the increasing flip graph on acyclic pipe dreams with exiting permutation is a lattice quotient of the interval of the weak ord…
A quantum Murnaghan--Nakayama rule for the flag manifold
Carolina Benedetti, Nantel Bergeron, Laura Colmenarejo +2
In this paper, we give a rule for the multiplication of a Schubert class by a tautological class in the (small) quantum cohomology ring of the flag manifold. As an intermediate ste…