133 citations · 554 across the 117 of their papers we have counts for
7 papers · 1 filter
Hopf structures on the multiplihedra
Stefan Forcey, Aaron Lauve, Frank Sottile
We investigate algebraic structures that can be placed on vertices of the multiplihedra, a family of polytopes originating in the study of higher categories and homotopy theory. Mo…
Khovanskii-Rolle continuation for real solutions
Dan Bates, Frank Sottile
We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of t…
New Hopf Structures on Binary Trees (Extended Abstract)
Stefan Forcey, Aaron Lauve, Frank Sottile
The multiplihedra {M_n} form a family of polytopes originating in the study of higher categories and homotopy theory. While the multiplihedra may be unfamiliar to the algebraic com…
Frontiers of Reality in Schubert Calculus
Frank Sottile
The theorem of Mukhin, Tarasov, and Varchenko (formerly the Shapiro conjecture for Grassmannians) asserts that all (a priori complex) solutions to certain geometric problems in the…
Skew Littlewood-Richardson rules from Hopf algebras
Thomas Lam, Aaron Lauve, Frank Sottile
We use Hopf algebras to prove a version of the Littlewood-Richardson rule for skew Schur functions, which implies a conjecture of Assaf and McNamara. We also establish skew Littlew…
Experimentation at the Frontiers of Reality in Schubert Calculus
Christopher Hillar, Luis Garcia-Puente, Abraham Martin del Campo +4
We describe a general framework for large-scale computational experiments in mathematics using computer resources that are available in most mathematics departments. This framework…
Fewnomial bounds for completely mixed polynomial systems
Frederic Bihan, Frank Sottile
We give a bound for the number of real solutions to systems of n polynomials in n variables, where the monomials appearing in different polynomials are distinct. This bound is smal…