19 citations · 101 across the 28 of their papers we have counts for
36 papers
Introduction to the Cohomology of the Flag Variety
Sara C. Billey, Yibo Gao, Brendan Pawlowski
One hundred years ago, Hilbert gave a list of important open problems in mathematics. His 15th problem asked for the development of a rigorous calculus explaining Schubert's enumer…
Generalized rank functions and quilts of alternating sign matrices
Sara Billey, Matjaž Konvalinka
In this paper, we present new objects, quilts of alternating sign matrices with respect to two given posets. Quilts generalize several commonly used concepts in mathematics. For ex…
Cyclotomic generating functions
Sara C. Billey, Joshua P. Swanson
It is a remarkable fact that for many statistics on finite sets of combinatorial objects, the roots of the corresponding generating function are each either a complex root of unity…
Criteria for smoothness of Positroid varieties via pattern avoidance, Johnson graphs, and spirographs
Sara C. Billey, Jordan E. Weaver
Positroids are certain representable matroids originally studied by Postnikov in connection with the totally nonnegative Grassmannian and now used widely in algebraic combinatorics…
A Pattern Avoidance Characterization for Smoothness of Positroid Varieties
Sara C. Billey, Jordan E. Weaver
Positroids are certain representable matroids originally studied by Postnikov in connection with the totally nonnegative Grassmannian and now used widely in algebraic combinatorics…
The metric space of limit laws for -hook formulas
Sara C. Billey, Joshua P. Swanson
In earlier work, Billey--Konvalinka--Swanson studied the asymptotic distribution of the coefficients of Stanley's -hook length formula, or equivalently the major index on standa…