 He then applied this symbolic calculus to combinatorial analysis, Bernoulli numbers, difference equations, differential equations, and summability factors.In 1951 he published a further two short papers Sur l'inversion des transformateurs and Sur une théorie ensembliste des jeux alternatifs  that announced various results that would be discussed fully in his thesis.He was awarded a doctorate in 1953 for his thesis Sur une théorie ensembliste des jeux alternatifs.