1,647 research outputs found

    Permutations avoiding certain patterns: The case of length 4 and some generalizations

    Get PDF
    AbstractProving and disproving some earlier conjectures, we give a characterization of the numbers of permutations avoiding each pattern of length 4. Some implications for longer patterns are included

    Some Triangulated Surfaces without Balanced Splitting

    Full text link
    Let G be the graph of a triangulated surface Σ\Sigma of genus g≥2g\geq 2. A cycle of G is splitting if it cuts Σ\Sigma into two components, neither of which is homeomorphic to a disk. A splitting cycle has type k if the corresponding components have genera k and g-k. It was conjectured that G contains a splitting cycle (Barnette '1982). We confirm this conjecture for an infinite family of triangulations by complete graphs but give counter-examples to a stronger conjecture (Mohar and Thomassen '2001) claiming that G should contain splitting cycles of every possible type.Comment: 15 pages, 7 figure

    Using the coral System to Discover Attacks on Security Protocols

    Get PDF
    • …
    corecore