Transformation of the Catalan Numbers and Related Counted Sets
Abstract
Borel's triangle is a triangular array of numbers constructed by a transformation of the Catalan numbers. By identifying natural bijections between them, we discuss several sets counted by Borel's triangle, including full binary trees with a fixed number of "marked" branching vertices, ballot sequences in elections between three parties, and permutations with a given set of properties. We further introduce a strategy which can be used to identify more combinatorial interpretations of Borel's triangle.
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- OSU Theses [15752]