9 citations · 16 across the 6 of their papers we have counts for
6 papers · 1 filter
Euler Characteristic of real nondegenerate tropical complete intersections
Benoit Bertrand, Frederic Bihan
We define nondegenerate tropical complete intersections imitating the corresponding definition in complex algebraic geometry. As in the complex situation, all nonzero intersection…
Bounds on the number of real solutions to polynomial equations
Daniel J. Bates, Frédéric Bihan, Frank Sottile
We use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound (e^4+3) 2^(k choose 2) n^k/4 for the…
Gale duality for complete intersections
Frédéric Bihan, Frank Sottile
We show that every complete intersection of Laurent polynomials in an algebraic torus is isomorphic to a complete intersection of master functions in the complement of a hyperplane…
On the Sharpness of fewnomial bound and the number of components of a fewnomial hypersurface
Frederic Bihan, J. Maurice Rojas, Frank Sottile
We show the existence of systems of n polynomial equations in n variables, with a total of n+k+1 distinct monomial terms, possessing [n/k+1]^k nondegenerate positive solutions. (He…
Polynomial systems supported on circuits and dessins d'enfants
F. Bihan
We study polynomial systems whose equations have as common support a set C of n+2 points in Z^n called a circuit. We find a bound on the number of real solutions to such systems wh…
First Steps in Algorithmic Fewnomial Theory
Frederic Bihan, J. Maurice Rojas, Casey E. Stella
Fewnomial theory began with explicit bounds -- solely in terms of the number of variables and monomial terms -- on the number of real roots of systems of polynomial equations. Here…