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arXiv · 1805.06077

Increasing Consecutive Patterns in Words

Mingjia Yang·Doron Zeilberger
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Abstract

We show how to enumerate words in $1^{m_1} \dots n^{m_n}$ that avoid the increasing consecutive pattern $12 \dots r$ for any $r \geq 2$. Our approach yields an $O(n^{s+1})$ algorithm to enumerate words in $1^s \dots n^s$, avoiding the consecutive pattern $1\dots r$, for any $s$, and any $r$. This enables us to supply many more terms to quite a few OEIS sequences, and create new ones. We also treat the more general case of counting words with a specified number of the pattern of interest (the avoiding case corresponding to zero appearances). This article is accompanied by three Maple packages implementing our algorithms.

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Mingjia Yang, Doron Zeilberger. 2018-05-16. Increasing Consecutive Patterns in Words. https://arxiv.org/abs/1805.06077

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