23 citations · 43 across the 33 of their papers we have counts for
4 papers · 1 filter
Solutions of the Braid Equation with set-type square
Jorge Alberto Guccione, Juan José Guccione, Christian Valqui
For a family of height one orders and each non-degenerate solution of the set-theoretic braid equation on satisfying su…
Some algorithms related to the Jacobian Conjecture
Jorge A. Guccione, Juan J. Guccione, Rodrigo Horruitiner +1
We describe an algorithm that computes possible corners of hypothetical counterexamples to the Jacobian Conjecture up to a given bound. Using this algorithm we compute the possible…
The Jacobian Conjecture: Approximate roots and intersection numbers
Jorge Alberto Guccione, Juan José Guccione, Rodrigo Horruitiner +1
We translate the results of Yansong Xu into the language of~\cite{GGV1}, obtaining nearly the same formulas for the intersection number of Jacobian pairs, but with an inequality in…
Solutions of the braid equation and orders
Jorge Alberto Guccione, Juan José Guccione, Christian Valqui
We introduce the notion of a non-degenerate solution of the braid equation on the incidence coalgebra of a locally finite order. Each one of these solutions induce by restriction a…