# 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} }

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…

## 3 Citations

Exact and asymptotic enumeration of cyclic permutations according to descent set

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- 2019

A simple formula is found for the number of cyclic permutations with a given descent set, by expressing it in terms of ordinary descent numbers, which shows that, for almost all sets I ⊆ [ n − 1 ] , the fraction of size-n permutation with descent set I which are n-cycles is asymptotically 1 / n.

Reciprocals of exponential polynomials and permutation enumeration

- Computer Science, MathematicsAustralas. J Comb.
- 2019

We show that the reciprocal of a partial sum with 2m terms of the alternating exponential series is the exponential generating function for permutations in which every increasing run has length…

Stirling permutations containing a single pattern of length three

- Computer ScienceAustralas. J Comb.
- 2019

We derive explicit formulæ for the number of k-Stirling permutations containing a single occurrence of a single pattern of length three as well as expressions for the corresponding generating…

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