Corpus ID: 235458407

Efficient recurrence for the enumeration of permutations with fixed pinnacle set

@inproceedings{Fang2021EfficientRF,
  title={Efficient recurrence for the enumeration of permutations with fixed pinnacle set},
  author={W. Fang},
  year={2021}
}
Initiated by Davis, Nelson, Petersen and Tenner (2018), the enumerative study of pinnacle sets of permutations has attracted a fair amount of attention recently. In this article, we provide a recurrence that can be used to compute efficiently the number |Sn(P)| of permutations of size n with a given pinnacle set P, with arithmetic complexity O(k4 + k log n) for P of size k. A symbolic expression can also be computed in this way for pinnacle sets of fixed size. A weighted sum qn(P) of |Sn(P… Expand
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Pinnacle sets revisited
In 2017, Davis, Nelson, Petersen, and Tenner [Discrete Math. 341 (2018),3249–3270] initiated the combinatorics of pinnacles in permutations. We provide a simple and efficient recursion to computeExpand

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