论文信息 - Pascal triangles, Catalan numbers and renewal arrays

Pascal triangles, Catalan numbers and renewal arrays

Abstract In response to some recent questions of L.W. Shapiro, we develop a theory of triangular arrays, called renewal arrays, which have arithmetic properties similar to those of Pascal's triangle. The Lagrange inversion formula has an important place in this theory and there is a close relation between it and the theory of renewal sequences. By way of illustration, we give several examples of renewal arrays of combinatorial interest, including complete generalizations of the familiar Pascal triangle and sequence of Catalan numbers.

D. G. Rogers | D. Rogers | Douglas G. Rogers

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