133 citations · 1.4k across the 77 of their papers we have counts for
79 papers
Finite noncommutative coinvariant algebras
Farid Aliniaeifard, Nantel Bergeron, Huilan Li +1
We study quotients of free associative algebras by the two-sided ideals generated by positive-degree symmetric, quasisymmetric, or free quasisymmetric polynomials. Free quasisymmet…
A memorial tribute: Adriano Garsia (1928--2024)
Hélène Barcelo, François Bergeron, Nantel Bergeron +15
Adriano Mario Garsia was born in Tunis on August 20, 1928, to a Tunisian-Italian family. He lived on a farm there until the end of World War II, then moved to Rome. After finishing…
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…
The Quasisymmetric Grassmannian
Nantel Bergeron, Lucas Gagnon, Hunter Spink +1
We construct a complex of toric varieties we call the quasisymmetric Grassmannian inside the Grassmannian of -planes in . Each irreducible component is a positroid…
The Coxeter Flag Variety
Nantel Bergeron, Lucas Gagnon, Hunter Spink +1
For a Coxeter element in a Weyl group , we define the -Coxeter flag variety as the union of left-translated Richardson varieties $w^{-1}…
The quasisymmetric flag variety: a toric complex on noncrossing partitions
Nantel Bergeron, Lucas Gagnon, Philippe Nadeau +2
We develop the geometric theory of equivariant quasisymmetry via a new ``quasisymmetric flag variety''. This is a toric complex in the flag variety whose fixed point set is the set…
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…
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 …
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…
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 order.…
The excedance quotient of the Bruhat order, Quasisymmetric Varieties and Temperley-Lieb algebras
Nantel Bergeron, Lucas Gagnon
Let be the ring of polynomial in variables and consider the ideal generated by quasisym…
Quasisymmetric harmonics of the exterior algebra
Nantel Bergeron, Kelvin Chan, Farhad Soltani +1
We study the ring of quasisymmetric polynomials in anticommuting (fermionic) variables. Let denote the polynomials in anticommuting variables. The main results of thi…
{T}he Gröbner Basis of a Catalan Path Ideal
Nantel Bergeron, Xavier Mootoo, Vedarth Vyas
For the ideal in with char() = 0, we show that the reduced Gröbner basi…
Hopf algebras of parking functions and decorated planar trees
Nantel Bergeron, Rafael S. González D'León, Shu Xiao Li +2
We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled…
Sign variation and descents
Nantel Bergeron, Aram Dermenjian, John Machacek
For any and , let be the poset of projective equivalence classes of -vectors of length with sign variation bounded by , ordered by…
Elliptic and -Analogs of the Fibonomial Numbers
Nantel Bergeron, Cesar Ceballos, Josef Küstner
In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial numbers, integer numbers that are obtained from the binomial coefficients by replacing each term by it…
New Invariants for Permutations, Orders and Graphs
Jean-christophe Aval, Nantel Bergeron, John Machacek
We study the symmetric function and polynomial combinatorial invariants of Hopf algebras of permutations, posets and graphs. We investigate their properties and the relations among…
Flagged -partitions
Sami Assaf, Nantel Bergeron
We introduce the theory of -partitions, depending on a poset and a map from to positive integers. The generating function $\mathfra…
Hopf dreams and diagonal harmonics
Nantel Bergeron, Cesar Ceballos, Vincent Pilaud
This paper introduces a Hopf algebra structure on a family of reduced pipe dreams. We show that this Hopf algebra is free and cofree, and construct a surjection onto a commutative…
Stable set polytopes and their 1-skeleta
Farid Aliniaeifard, Carolina Benedetti, Nantel Bergeron +2
We characterize the edges of two classes of -polytopes. The first class corresponds to the stable set polytope of a graph and includes chain polytopes of posets, some inst…
Hypergraphic polytopes: combinatorial properties and antipode
Carolina Benedetti, Nantel Bergeron, John Machacek
In an earlier paper, the first two authors defined orientations on hypergraphs. Using this definition we provide an explicit bijection between acyclic orientations in hypergraphs a…
Cancelation free formula for the antipode of linearized Hopf monoid
Nantel Bergeron, Carolina Benedetti
Many combinatorial Hopf algebras in the literature are the functorial image of a linearized Hopf monoid . That is, or $H=\overline{\mathcal K}…
A Hopf algebra of subword complexes
Nantel Bergeron, Cesar Ceballos
We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acycli…
A combinatorial proof that Schubert vs. Schur coefficients are nonnegative
Sami Assaf, Nantel Bergeron, Frank Sottile
We give a combinatorial proof that the product of a Schubert polynomial by a Schur polynomial is a nonnegative sum of Schubert polynomials. Our proof uses Assaf's theory of dual eq…