Um estudo sobre a paridade da soma de coeficientes binomiais

Abstract

The binomial coefficients appear in many areas of mathematics, and the characterization of a formula to determine the sum of consecutive binomial coefficients in a row of Pascal’s Triangle still remains a problem without a solution. There are several significant interpretations of the sum of binomial coefficients in different fields of research, as in information theory, coding theory, discrete geometry and combinatorics. This work has as goal to analyze the parity of the sum of binomial coefficients in a row of Pascal’s Triangle, presenting a review of the contribution of important mathematicians, such as Blaise Pascal and François Lucas, to the theme. Furthermore, it is presented an application of the parity of binomial coefficients in the study of the parity of RT-balls. Therefore, a bibliographic review of the works published by researchers in the field was carried out, thus bringing together the results already achieved over time. Significant results of parity characterization of the sum of binomial coefficients are presented, however, the problem remains open, and it can be investigated in the future.