SOLUCIÓN AL PROBLEMA COMBINATORIO USANDO UNA FUNCIÓN DE CLASE HÖLDER

Abstract

A combinatorial problem on the distribution and common area of inscribed squares is considered. In this paper we propose to investigate this problem based on the properties of Hölder functions. Peano curve gives us an example of a continuous curve that has the measure of the set of its graphic points greater than zero. All differentiable curves have the measure zero. Hölder curves are "better" than the continuous curves and "worse" than differentiable curves, they occupy intermediate positions. All the Hölder curves with the exponent greater than ½ have the measure zero. In this work, based on the Sierpinski carpet, we constructed a Hölder curve with the exponent ½, and the measure greater than zero. The considered combinatorial problem is solved through the properties of this curve.