4 papers
Khovanskii's Bezout-type Theorem for Pfaffian Functions: A Self-Contained Proof, and Applications
Martin Lotz, Abhiram Natarajan
We present a direct and self-contained proof of Khovanskii's Bezout-type bound for the number of nondegenerate solutions of a system of Pfaffian equations. We isolate the ingredien…
Parameterwise Sharpness of Khovanskii's Bezout-type Bound for Pfaffian Functions
Terence Bickerton, Joseph Harrison, Olivia Hornakova +3
Khovanskii's theorem gives a Bezout-type upper bound for the number of isolated real solutions of a system of Pfaffian equations in variables in terms of three complexity p…
Gröbner Bases Native to Term-ordered Commutative Algebras, with Application to the Hodge Algebra of Minors
Joshua A. Grochow, Abhiram Natarajan
Motivated by better understanding the bideterminant (=product of minors) basis on the polynomial ring in variables, we develop theory \& algorithms for Gröbner bases…
Distinct Distances on Pfaffian Curves
Abhiram Natarajan, Adam Sheffer
We generalize Pach and de Zeeuw's bound for distinct distances between points on two curves, from algebraic curves to Pfaffian curves. Pfaffian curves include those that can be def…