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Islands on a triangular grid
by
Gabriella Pluhár
Eötvös Loránd University, Budapest
Coauthors: Eszter K. Horváth, Zoltán Németh
We solve a purely combinatorial problem via algebraic tools. For every triangular unit of a triangular grid a real number is given, its height. A triangle on the grid is called a triangular island iff the height of every triangular unit of the triangle is bigger than the height of the adjacent triangular units. In other words, if there exists a possible water-level by which the triangle is an island in the usual sense.
We give a lower and an upper estimates for the maximum of the number of triangular islands. For determining the upper bound a lattice theoretical theorem of Czédli, Huhn and Schmidt is applied.
Date received: May 5, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawc-44.