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arXiv · 2607.19410

Counting words without non-decreasing subwords of fixed length

Senan Sekhon
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Abstract

In arXiv:2511.13287, we derived exact formulas for generating functions counting the number of $n$-ary words avoiding \textit{strictly} increasing subwords of length $k$, and provided applications in probability theory as well as the continuous limit as $n\to\infty$. We also conjectured several corresponding formulas for the case where the ``strictly'' requirement is dropped. In this paper, we prove those formulas.

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Senan Sekhon. 2026-07-12. Counting words without non-decreasing subwords of fixed length. https://arxiv.org/abs/2607.19410

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