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A determinant representation for generalized ballot and Fuss-Catalan numbers

In this note we introduce a determinant and then give its evaluating formula. The determinant turns out to be a generalization of the well-known ballot and Fuss-Catalan numbers, which is believed to be new. The evaluating formula is proved by showing that the determinant coincides with the number of lattice paths with (1,0), (0,1)-steps in the plane that stay below a boundary line of rational slope.

preprint2013arXivOpen access
James J. Y. Zhao
math.CO
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James J. Y. Zhao

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