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Enumerations of Permutations by Circular Descent Sets | | Hungyung Chang
; Jun Ma
; Yeong-Nan Yeh
; | | Date: |
3 Jun 2008 | | Abstract: | The circular descent of a permutation $sigma$ is a set ${sigma(i)mid
sigma(i)>sigma(i+1)}$. 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. | | Source: | arXiv, 0806.0433 | | Services: | Forum | Review | PDF | Favorites | |
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