Separation Probabilities for Products of Permutations
We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements 1,2,. . .,k are in distinct cycles of the random permutation of {1,2,. . .,n} obtained as a product...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Cambridge University Press
2015
|
| Online Access: | http://hdl.handle.net/1721.1/93190 https://orcid.org/0000-0003-3123-8241 |
| _version_ | 1826189646320631808 |
|---|---|
| author | Bernardi, Olivier Du, Rosena R. X. Morales, Alejandro H. Stanley, Richard P. Bernardi, Olivier |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bernardi, Olivier Du, Rosena R. X. Morales, Alejandro H. Stanley, Richard P. Bernardi, Olivier |
| author_sort | Bernardi, Olivier |
| collection | MIT |
| description | We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements 1,2,. . .,k are in distinct cycles of the random permutation of {1,2,. . .,n} obtained as a product of two uniformly random n-cycles. |
| first_indexed | 2024-09-23T08:18:54Z |
| format | Article |
| id | mit-1721.1/93190 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:18:54Z |
| publishDate | 2015 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | mit-1721.1/931902022-09-30T08:55:59Z Separation Probabilities for Products of Permutations Bernardi, Olivier Du, Rosena R. X. Morales, Alejandro H. Stanley, Richard P. Bernardi, Olivier Massachusetts Institute of Technology. Department of Mathematics Stanley, Richard P. Bernardi, Olivier Morales, Alejandro H. We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements 1,2,. . .,k are in distinct cycles of the random permutation of {1,2,. . .,n} obtained as a product of two uniformly random n-cycles. National Science Foundation (U.S.) (Grant DMS-1308441) ERC Explore-Maps Centre de recherches mathématiques. Institut des sciences mathématiques (CRM-ISM) Postdoctoral Fellowship 2015-01-29T16:17:57Z 2015-01-29T16:17:57Z 2013-12 2013-09 Article http://purl.org/eprint/type/JournalArticle 0963-5483 1469-2163 http://hdl.handle.net/1721.1/93190 Bernardi, Olivier, Rosena R. X. Du, Alejandro H. Morales, and Richard P. Stanley. “Separation Probabilities for Products of Permutations.” Combinatorics, Probability and Computing 23, no. 02 (December 13, 2013): 201–222. https://orcid.org/0000-0003-3123-8241 en_US http://dx.doi.org/10.1017/S0963548313000588 Combinatorics Probability and Computing Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Cambridge University Press arXiv |
| spellingShingle | Bernardi, Olivier Du, Rosena R. X. Morales, Alejandro H. Stanley, Richard P. Bernardi, Olivier Separation Probabilities for Products of Permutations |
| title | Separation Probabilities for Products of Permutations |
| title_full | Separation Probabilities for Products of Permutations |
| title_fullStr | Separation Probabilities for Products of Permutations |
| title_full_unstemmed | Separation Probabilities for Products of Permutations |
| title_short | Separation Probabilities for Products of Permutations |
| title_sort | separation probabilities for products of permutations |
| url | http://hdl.handle.net/1721.1/93190 https://orcid.org/0000-0003-3123-8241 |
| work_keys_str_mv | AT bernardiolivier separationprobabilitiesforproductsofpermutations AT durosenarx separationprobabilitiesforproductsofpermutations AT moralesalejandroh separationprobabilitiesforproductsofpermutations AT stanleyrichardp separationprobabilitiesforproductsofpermutations AT bernardiolivier separationprobabilitiesforproductsofpermutations |