Comming seminars

  • Laszlo Szalay (Mathematical Institute, University of West Hungary, Sopron): Survey on hyperbolic Pascal triangles

    26.3.2018 14:00 @ Hora Informaticae

    There are several approaches to generalize Pascal's arithmetical triangle. One of them is associated to the hyperbolic plane, where there exist an infinite number of types of regular mosaics, they are assigned by Schlafli's symbol {p,q}, where the positive integers p and q satisfy (p-2)(q-2)>4. Each regular mosaic induces a so-called hyperbolic Pascal triangle, following and generalizing the connection between the classical Pascal's triangle and the Euclidean regular square mosaic {4,4}. A hyperbolic Pascal triangle can be figured as a digraph, where the vertices and the edges are the vertices and the edges of a well defined part of the lattice {p,q}, respectively, further each vertex possesses a value, say label, giving the number of different shortest paths from the fixed base vertex. In the presentation we survey the results on the subject matter.