Labeled Partitions with Colored Permutations
| Autor: | Chen, William Y. C., Gao, Henry Y., He, Jia |
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| Rok vydání: | 2008 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations in the sense that the colors are endowed with a cyclic structure. We use labeled partitions with colored permutations to derive the generating function of the $\mathrm{fmaj}_k$ indices of colored permutations. The second result is a combinatorial treatment of a relation on the q-derangement numbers with respect to colored permutations which leads to the formula of Chow for signed permutations and the formula of Faliharimalala and Zeng [10] on colored permutations. The third result is an involution on permutations that implies the generating function formula for the signed q-counting of the major indices due to Gessel and Simon. This involution can be extended to signed permutations. In this way, we obtain a combinatorial interpretation of a formula of Adin, Gessel and Roichman. Comment: 14 pages |
| Databáze: | arXiv |
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