In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular m-sided polygons inscribed in a circle. The result shows that the quantization coefficient for the uniform distribution on the boundary of a regular m-sided polygon inscribed in a circle is an increasing function of m, and approaches to the quantization coefficient for the uniform distribution on the circle as m tends to infinity.
Hansen, Joel, Itzamar Marquez, Mrinal K. Roychowdhury, and Eduardo Torres. 2020. “Quantization Coefficients for Uniform Distributions on the Boundaries of Regular Polygons.” ArXiv:2008.02681 [Math], August. http://arxiv.org/abs/2008.02681.