Rigoberto Flórez

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We construct a formal power series on several variables that encodes many statistics on non-decreasing Dyck paths. In particular, we use this formal power series to count peaks, pyramid weights, and indexed sums of pyramid weights for all non-decreasing Dyck paths of length 2n. We also show that an indexed sum on pyramid weights depends only on the size and(More)
The Hosoya polynomial triangle is a triangular arrangement of polynomials where each entry is a product of two polynomials. The geometry of this triangle is a good 1 tool to study the algebraic properties of polynomial products. In particular, we find closed formulas for the alternating sum of products of polynomials such as Fibonacci polynomials, Chebyshev(More)
In a social network individuals have prominent centrality if they are intermediaries between the communication of others. The betweenness centrality of a vertex measures the number of intersecting geodesics between two other vertices. Formally, the betweenness centrality of a vertex v is the ratio of the number of shortest paths between two other vertices u(More)
The generalized Hosoya triangle is an arrangement of numbers where each entry is a product of two generalized Fibonacci numbers. We define a discrete convolution 1 C based on the entries of the generalized Hosoya triangle. We use C and generating functions to prove that the sum of every k-th entry in the n-th row or diagonal of generalized Hosoya triangle,(More)
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