The expected number of inversions after n adjacent transpositions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2009
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| _version_ | 1866914054604324864 |
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| author | Bousquet-Mélou, Mireille |
| author_facet | Bousquet-Mélou, Mireille |
| contents | We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group S_{m+1}. We then derive from this expression the asymptotic behaviour of this number when n scales with m in various ways. Our starting point is an equivalence, due to Eriksson et al., with a problem of weighted walks confined to a triangular area of the plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0909_0103 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | The expected number of inversions after n adjacent transpositions Bousquet-Mélou, Mireille Combinatorics Probability 05A05, 05A15, 05A16, 60J10 We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group S_{m+1}. We then derive from this expression the asymptotic behaviour of this number when n scales with m in various ways. Our starting point is an equivalence, due to Eriksson et al., with a problem of weighted walks confined to a triangular area of the plane. |
| title | The expected number of inversions after n adjacent transpositions |
| topic | Combinatorics Probability 05A05, 05A15, 05A16, 60J10 |
| url | https://arxiv.org/abs/0909.0103 |