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arXiv · 2503.02005

A formula for the number of up-down words

Sela Fried
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Abstract

A word $w_1w_2\cdots w_n$ is said to be up-down if $w_1 < w_2 >w_3 \cdots$. Carlitz and Scoville found the generating function for the number of up-down words over an alphabet of size $k$. Using properties of the Chebyshev polynomials we derive a closed-form formula for these numbers.

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Sela Fried. 2025-04-08. A formula for the number of up-down words. https://arxiv.org/abs/2503.02005

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