3 citations · 9 across the 8 of their papers we have counts for
8 papers
Simple formulas for lattice paths avoiding certain periodic staircase boundaries
Robin J. Chapman, Timothy Y. Chow, Amit Khetan +2
There is a strikingly simple classical formula for the number of lattice paths avoiding the line x = ky when k is a positive integer. We show that the natural generalization of thi…
Solving the Likelihood Equations
Serkan Hosten, Amit Khetan, Bernd Sturmfels
Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all cr…
The Maximum Likelihood Degree
Fabrizio Catanese, Serkan Hosten, Amit Khetan +1
Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this o…
Combinatorial construction of toric residues
Amit Khetan, Ivan Soprounov
The toric residue is a map depending on n+1 semi-ample divisors on a complete toric variety of dimension n. It appears in a variety of contexts such as sparse polynomial systems, m…
Implicitization of rational surfaces using toric varieties
Amit Khetan, Carlos D'Andrea
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend t…
Exact matrix formula for the unmixed resultant in three variables
Amit Khetan
We give the first exact determinantal formula for the resultant of an unmixed sparse system of four Laurent polynomials in three variables with arbitrary support. This follows earl…