Ballot matrix as Catalan matrix power and related identities

作者：Stanimirovic Stefan; Stanimirovic Predrag^*; Ilic Aleksandar

来源：Discrete Applied Mathematics, 2012, 160(3): 344-351.

DOI：10.1016/j.dam.2011.10.016

• Ballot number
• Ballot matrix
• Catalan number
• Catalan matrix
• Generalized hypergeometric function
• Generating function

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/(similar to)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.

• 出版日期2012-2