Enumerations for Permutations by Circular Peak Sets

Details Enumerations for Permutations by Circular Peak Sets Enumerations for Permutations by Circular Peak Sets

2008-06-03

arxiv.org/abs/0806.0435v2

Mathematics

Combinatorics

Scientific paper

The circular peak set of a permutation $\sigma$ is the set $\{\sigma(i)\mid \sigma(i-1)<\sigma(i)>\sigma(i+1)\}$. In this paper, we focus on the enumeration problems for permutations by circular peak sets. Let $cp_n(S)$ denote the number of the permutations of order $n$ which have the circular peak set $S$. For the case with $|S|=0,1,2$, we derive the explicit formulas for $cp_n(S)$. We also obtain some recurrence relations for the sequence $cp_n(S)$ and give the formula for $cp_n(S)$ in the general case.

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