2 citations · 4 across the 7 of their papers we have counts for
9 papers
Variations of the Catalan numbers from some nonassociative binary operations
Nickolas Hein, Jia Huang
We investigate certain nonassociative binary operations that satisfy a four-parameter generalization of the associative law. From this we obtain variations of the ubiquitous Catala…
Modular Catalan Numbers
Nickolas Hein, Jia Huang
The Catalan number enumerates parenthesizations of where is a binary operation. We introduce the modular Catalan number to count equivalence cl…
A lifted square formulation for certifiable Schubert calculus
Nickolas Hein, Frank Sottile
Formulating a Schubert problem as the solutions to a system of equations in either Plücker space or in the local coordinates of a Schubert cell usually involves more equations than…
A primal-dual formulation for certifiable computations in Schubert calculus
Jonathan D. Hauenstein, Nickolas Hein, Frank Sottile
Formulating a Schubert problem as the solutions to a system of equations in either Plücker space or in the local coordinates of a Schubert cell typically involves more equations th…
Lower Bounds in Real Schubert Calculus
Nickolas Hein, Christopher J. Hillar, Frank Sottile
We describe a large-scale computational experiment to study structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Sc…
Reality and Computation in Schubert Calculus
Nickolas Hein
The Mukhin-Tarasov-Varchenko Theorem (previously the Shapiro Conjecture) asserts that a Schubert problem has all solutions distinct and real if the Schubert varieties involved oscu…
Certifiable Numerical Computations in Schubert Calculus
Jonathan D. Hauenstein, Nickolas Hein, Frank Sottile
Traditional formulations of geometric problems from the Schubert calculus, either in Plucker coordinates or in local coordinates provided by Schubert cells, yield systems of polyno…
The monotone secant conjecture in the real Schubert calculus
Nickolas Hein, Christopher J. Hillar, Abraham Martin del Campo +2
The monotone secant conjecture posits a rich class of polynomial systems, all of whose solutions are real. These systems come from the Schubert calculus on flag manifolds, and the…
The Secant Conjecture in the real Schubert calculus
Luis Garcia-Puente, Nickolas Hein, Christopher J. Hillar +4
We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian i…