Some statistics on Stirling permutations and Stirling derangements |
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Authors: | Guan-Huei Duh Yen-Chi Roger Lin Shi-Mei Ma Yeong-Nan Yeh |
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Institution: | 1. Institute of Mathematics, Academia Sinica, Taipei, Taiwan;2. Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan;3. School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Hebei 066004, PR China |
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Abstract: | A permutation of the multiset is called a Stirling permutation of order if every entry between the two occurrences of is greater than for each . In this paper, we introduce the definitions of block, even indexed entry, odd indexed entry, Stirling derangement, marked permutation and bicolored increasing binary tree. We first study the joint distribution of ascent plateaux, even indexed entries and left-to-right minima over the set of Stirling permutations of order . We then present an involution on Stirling derangements. |
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Keywords: | Stirling permutations Marked permutations Stirling derangements Increasing trees |
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