Coxeter groups are of central importance in several areas of algebra, geometry, and
combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of …

A combinatorial Hopf algebra is a graded connected Hopf algebra over a field is the product
(in the categorical sense) of its even and odd Hopf subalgebras. We also calculate the odd …

While the intersection of the Grassmannian Bruhat decompositions for all coordinate flags is
an intractable mess, it turns out that the intersection of only the cyclic shifts of one Bruhat …

Algebraic combinatorics is concerned with the interaction between combinatorics and such
other branches of mathematics as commutative algebra, algebraic geometry, algebraic …

We prove that any three-point genus zero Gromov-Witten invariant on a type $ A $
Grassmannian is equal to a classical intersection number on a two-step flag variety. We also …

While the projections of Schubert varieties in a full generalized flag manifold G/B to a partial
flag manifold G/P are again Schubert varieties, the projections of Richardson varieties …

MEMOIRS Page 1 MEMOIRS of the American Mathematical Society Number 977 Affine
Insertion and Pieri Rules for the Affine Grassmannian Thomas Lam Luc Lapointe Jennifer …

This paper studies the geometry of one-parameter specializations of subvarieties of
Grassmannians and two-step flag varieties. As a consequence, we obtain a positive …

We prove that the Schubert structure constants of the quantum $ K $-theory ring of any
minuscule flag variety or quadric hypersurface have signs that alternate with codimension …

We study a basis of the polynomial ring that we call forest polynomials. This family of
polynomials is indexed by a combinatorial structure called indexed forests and permits …