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Quasi-translations and counterexamples to the Homogeneous Dependence Problem
In this article, the author gives counterexamples to the Linear Dependence Problem for Homogeneous Nilpotent Jacobians for dimension 5 and up. This problem has been formulated as a conjecture/problem
Some remarks on the Jacobian conjecture and polynomial endomorphisms
In this paper, we first show that homogeneous Keller maps are injective on lines through the origin. We subsequently formulate a generalization, which is that under some conditions, a polynomial
Triangularization properties of power linear maps and the Structural Conjecture
In this paper, we discuss several additional properties a power linear Keller map may have. The Structural Conjecture by Druuzkowski in [Dru] asserts that two such properties are equivalent, but we
A reduction of the Jacobian conjecture to the symmetric case
The main result of this paper asserts that it suffices to prove the Jacobian Conjecture for all polynomial maps of the form x + H, where H is homogeneous (of degree 3) and JH is nilpotent and
The computational complexity of Minesweeper
It is shown that the Minesweeper game is PP-hard, when the object is to locate all mines with the highest probability, and determining the solvability of a partially uncovered Minesweep board is NP-complete with hexagonal and triangular grids as well as a square grid.
Irreducibility properties of Keller maps
Jedrzejewicz showed that a polynomial map over a field of characteristic zero is invertible, if and only if the corresponding endomorphism maps irreducible polynomials to irreducible polynomials.
Homogeneous Keller maps
Quadratic polynomial maps with Jacobian rank two
  • M. D. Bondt
  • Mathematics
    Linear Algebra and its Applications
  • 4 January 2016