Enumerations for Permutations by Circular Peak Sets
Pierre Bouchard, Hungyung Chang, Jun Ma, Jean Yeh

TL;DR
This paper studies the enumeration of permutations based on their circular peak sets, providing explicit formulas, recurrence relations, and general formulas for various cases.
Contribution
It introduces explicit formulas and recurrence relations for counting permutations with specific circular peak sets, advancing combinatorial enumeration methods.
Findings
Derived explicit formulas for permutations with 0, 1, 2 circular peaks.
Established recurrence relations for the sequence $cp_n(S)$.
Provided a general formula for counting permutations by circular peak sets.
Abstract
The circular peak set of a permutation is the set . In this paper, we focus on the enumeration problems for permutations by circular peak sets. Let denote the number of the permutations of order which have the circular peak set . For the case with , we derive the explicit formulas for . We also obtain some recurrence relations for the sequence and give the formula for in the general case.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · semigroups and automata theory · Advanced Mathematical Identities
