Periodic de Bruijn triangles: exact and asymptotic results

@article{Shapiro2005PeriodicDB,
  title={Periodic de Bruijn triangles: exact and asymptotic results},
  author={Boris Z. Shapiro and Michael Shapiro and Alek Vainshtein},
  journal={Discrete Mathematics},
  year={2005},
  volume={298},
  pages={321-333}
}
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution. Let σ = (σ 1 ,. .. , σ n) be a permutation of length n. We associate with σ its up-down sequence (sometimes called the shape of σ, or the signature of σ) P(σ) = (p 1 ,. .. , p n−1), which is a binary vector of length n − 1 such that p i = 1 if σ i < σ i+1 and p i = 0 otherwise. During the… CONTINUE READING

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