Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
Some combinatorial identities via Fibonacci numbers
Discrete Applied Mathematics
Bernoulli matrix and its algebraic properties
Discrete Applied Mathematics
Note: A factorization of the symmetric Pascal matrix involving the Fibonacci matrix
Discrete Applied Mathematics
Note: Identities via Bell matrix and Fibonacci matrix
Discrete Applied Mathematics
Enumerative Combinatorics: Volume 1
Enumerative Combinatorics: Volume 1
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We use an analytical approach to find the kth power of the Catalan matrix. Precisely, it is proven that the power of the Catalan matrix is a lower triangular Toeplitz matrix which contains the well-known ballot numbers. A result from [H. S. Wilf, Generatingfunctionology, Academic Press, New York, 1990, Free download available from http://www.math.upenn.edu/~wilf/Downld.html.], related to the generating function for Catalan numbers, is extended to the negative integers. Three interesting representations for Catalan numbers by means of the binomial coefficients and the hypergeometric functions are obtained using relations between Catalan matrix powers.