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arXiv · 1809.07523

Catalan-like numbers and Hausdorff moment sequences

Hayoung Choi·Yeong-Nan Yeh·Seonguk Yoo
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Abstract

In this paper we show that many well-known counting coefficients, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the central Delannoy numbers are Hausdorff moment sequences in a unified approach. In particular we answer a conjecture of Liang at al. which such numbers have unique representing measures. The smallest interval including the support of representing measure is explicitly found. Subsequences of Catalan-like numbers are also considered. We provide a necessary and sufficient condition for a pattern of subsequences that if sequences are the Stieltjes Catalan-like numbers, then their subsequences are Stieltjes Catalan-like numbers. Moreover, a representing measure of a linear combination of consecutive Catalan-like numbers is studied.

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Hayoung Choi, Yeong-Nan Yeh, Seonguk Yoo. 2018-09-20. Catalan-like numbers and Hausdorff moment sequences. https://arxiv.org/abs/1809.07523

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