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In this paper, we introduce a generalization of Catalan numbers. To obtain this extension, we construct a family of subsets which depend on three parameters and whose cardinals originate it. The elements of this family are used to classify canonical primitive connected matrices of the p-Sylow of GLn(q), problem that is related to Higman’s Conjecture, which asserts that if Gn is the subgroup of GLn(q)...
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