Marco Ripà

Independent Researcher with a wide range of interests. Author of some number theory and graph theory papers (hyperoperators, paths and trails covering any d-dimensional hypercubic lattice, primality&factorization, and so forth). Elected Genius of the Year 2014 – Europe by members of the World Genius Directory and by the World Intelligence Network Executive Committee, mainly for his fundamental contribution to the creation of the first dynamic IQ tests. Enthusiastic contributor for the OEIS (father of 170+ integer sequences).

The Rectangular Spiral or the n_1 × n_2 × · · · × n_k Points Problem

  • Marco Ripà
    • Categories Bound-constrained Optimization, Combinatorial Optimization, Graphs and Matroids Tags , , , , , , ,

    A generalization of Ripà’s square spiral solution for the n × n × ··· × n Points Upper Bound Problem. Additionally, we provide a non-trivial lower bound for the k-dimensional n_1 × n_2 × ··· × n_k Points Problem. In this way, we can build a range in which, with certainty, all the best possible … Read more

    Minimum-Link Covering Trails for any Hypercubic Lattice

  • Marco Ripà
    • Categories Combinatorial Optimization, Graphs and Matroids Tags , , , , ,

    \(\) In 1994, Kranakis et al. published a conjecture about the minimum link-length of every rectilinear covering path for the \(k\)-dimensional grid \(P(n,k) := \{0,1, \dots, n-1\} \times \{0,1, \dots, n-1\} \times \cdots \times \{0,1, \dots, n-1\}\). In this paper we consider the general, NP-complete, Line-Cover problem, where the edges are not required to be … Read more