# Increasing consecutive patterns in words

```@article{Yang2019IncreasingCP,
title={Increasing consecutive patterns in words},
author={Mingjia Yang and Doron Zeilberger},
journal={Journal of Algebraic Combinatorics},
year={2019},
volume={51},
pages={89-101}
}```
• Published 16 May 2018
• Mathematics
• Journal of Algebraic Combinatorics
We show how to enumerate words in \$\$1^{m_1} \ldots n^{m_n}\$\$ 1 m 1 … n m n that avoid the increasing consecutive pattern \$\$12 \ldots r\$\$ 12 … r for any \$\$r \ge 2\$\$ r ≥ 2 . Our approach yields an \$\$O(n^{s+1})\$\$ O ( n s + 1 ) algorithm to enumerate words in \$\$1^s \ldots n^s\$\$ 1 s … n s , avoiding the consecutive pattern \$\$1\ldots r\$\$ 1 … 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…
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