About two decades ago we have shown mathematically that besides bosons and fermions, it could exist a third kind of particles in nature that was named gentileons. Our results have been obtained rigorously within the framework of quantum mechanics and the permutation group theory. However, these papers are somewhat intricate for physicists not familiarized with the permutation group theory. In the present paper we show in details, step by step, how to obtain our theoretical predictions. This was done in order to permit a clear understanding of our approach by graduate students with a basic knowledge of group theory. Keywords: quantum statistics; bosons, fermions and gentileons.Há cerca de duas décadas passadas, mostramos matematicamente que, além de bósons e férmions, poderia existir na natureza um outro tipo de partículas que denominamos de gentileons. Os nossos resultados foram obtidos rigorosamente dentro do contexto da mecânica quântica e da teoria do grupo de permutações. Entretanto, os nossos artigos são difíceis de serem entendidos por físicos que não estão familiarizados com a teoria do grupo de permutações. Assim, no presente artigo nós vamos mostrar em detalhes, passo a passo, como obter as nossas previsões. Procedemos desse modo para permitir que estudantes de graduação de física possam entender claramente nossos cálculos com um conhecimento básico de teoria de grupos. Palavras-chave: estatística quântica; bósons, férmions, gentileons.
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