arXiv (All)
open access
The Probability of Generating the Symmetric Group
We consider the probability $p(S_n)$ that a pair of random permutations generates either the alternating group $A_n$ or the symmetric group $S_n$. Dixon (1969) proved that $p(S_n)$ approaches $1$ as $n\to\infty$ and conjectured that $p(S_n)=1-1/n+o(1/n)$. This conjecture was verified by Babai (1989)
Conceptio Open Archive
Analyze & explore related research in Conceptio
Connect this record directly into your research workflow or AI agent. Explore citations across open repositories, query full text, and export structured proof bundles.
This document is indexed with metadata only: full text is not available in the archive for this record. Open the official source ↗
Related documents
- Some new classes of permutation polynomials and their compositional inverses#684174
- Some new classes of permutation polynomials and their compositional inverses#682399
- Eulerian calculus arising from permutation statistics#226750
- Normal subgroups of iterated wreath products of symmetric groups and alternating with symmetric groups#819198
- Normal subgroups of iterated wreath products of symmetric groups and alternating with symmetric groups#809206
Record · ID 925677
Retrieved via Conceptio: every document is proof-bundled with source, license, and retrieval metadata.
Retrieved via Conceptio: every document is proof-bundled with source, license, and retrieval metadata.
Bring this data into your agent: Connect via MCP or API · 20 free credits to start · no card required
Read the Docs → · View CLI source on GitHub · Conceptio Open Knowledge Archive
Read the Docs → · View CLI source on GitHub · Conceptio Open Knowledge Archive