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arXiv · 0806.0433

Enumerations of Permutations by Circular Descent Sets

Hungyung Chang·Jun Ma·Yeong-Nan Yeh
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Abstract

The circular descent of a permutation $σ$ is a set $\{σ(i)\mid σ(i)>σ(i+1)\}$. In this paper, we focus on the enumerations of permutations by the circular descent set. Let $cdes_n(S)$ be the number of permutations of length $n$ which have the circular descent set $S$. We derive the explicit formula for $cdes_n(S)$. We describe a class of generating binary trees $T_k $ with weights. We find that the number of permutations in the set $CDES_n(S)$ corresponds to the weights of $T_k$. As a application of the main results in this paper, we also give the enumeration of permutation tableaux according to their shape.

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BibTeXRIS

Hungyung Chang, Jun Ma, Yeong-Nan Yeh. 2008-06-05. Enumerations of Permutations by Circular Descent Sets. https://arxiv.org/abs/0806.0433

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