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**publisher and metadata sources**).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… Continue Reading

We show that the Minesweeper game is PP-hard, when the object is to locate all mines with the highest probability. When the probability of locating all mines may be infinitesimal, the Minesweeper… Continue Reading

Let H:Cn→Cn be a polynomial map such that the Jacobian JH of H is nilpotent and symmetric. The symmetric dependence problem, SDP(n), asks whether the rows of the matrix JH are dependent over C. We… Continue Reading

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… Continue Reading

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… Continue Reading

Let k be a field of characteristic zero and F : k 3 → k 3 a polynomial map of the form F = x + H , where H is homogeneous of degree d 2. We show that the Jacobian Conjecture is true for such… Continue Reading

We give a detailed proof for Gordan-Noether’s results in “Ueber die algebraischen Formen, deren Hesse’sche Determinante identisch verschwindet.” C. Lossen has written a paper in a similar direction… Continue Reading

It was conjectured by Cerný in 1964, that a synchronizing DFA on n states always has a synchronizing word of length at most \((n-1)^2\), and he gave a sequence of DFAs for which this bound is… Continue Reading

We first prove that solving Mahjong Solitaire boards with peeking is NP-complete, even if one only allows isolated stacks of the forms /aab/ and /abb/. We subsequently show that layouts of isolated… Continue Reading

It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is… Continue Reading