arXiv subjects
Publications and source records attributed to Zeina Ghazo Hanna.
We construct a combinatorial function F which computes the number of oriented Hamiltonian paths of any given type, in a transitive tournament. We also study many properties of F that arise, and reach some observations.
We prove that a tournament and its complement contain the same number of oriented Hamiltonian paths (resp. cycles) of any given type, as a generalization of Rosenfeld's result proved for antidirected paths.
We explore relations between cyclic sequences determined by a quadratic difference relation, cyclotomic polynomials, Eulerian digraphs and walks in the plane. These walks correspond to closed paths for which at each step one must turn either left or right through a fixed angle. In the case when this angle is $2 π/n$, then non-symmetric phenomena occurs for $n\geq 12$. Examples arise from algebraic numbers of modulus one which are not $n$'th roots of unity.