133 citations · 1.4k across the 77 of their papers we have counts for
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A Monoid for the Universal K-Bruhat Order
Nantel Bergeron, Frank Sottile
Structure constants for the multiplication of Schubert polynomials by Schur symmetric polynomials are known to be related to the enumeration of chains in a new partial order on S_\…
Hopf Algebras and Edge-Labeled Posets
Nantel Bergeron, Frank Sottile
Given a finite graded poset with labeled Hasse diagram, we construct a quasi- symmetric generating function for (saturated) chains whose labels have fixed descents. This is a commo…
Skew Schubert functions and the Pieri formula for flag manifolds
Nantel Bergeron, Frank Sottile
We show the equivalence of the Pieri formula for flag manifolds and certain identities among the structure constants, giving new proofs of both the Pieri formula and of these ident…
Identities of Structure Constants for Schubert polynomials and Orders on S_n
Nantel Bergeron, Frank Sottile
We use geometry to prove a number of new identities among the Littlewood-Richardson coefficients for Schubert polynomials (Schubert classes in a flag manifold). For many of these i…
Schubert polynomials, the Bruhat order, and the geometry of flag manifolds
Nantel Bergeron, Frank Sottile
We illuminate the relation between the Bruhat order on the symmetric group and structure constants (Littlewood-Richardson coefficients) for the cohomology of the flag manifold in t…