Timeline for The Odds 3 (or More) Group Elements Commute
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 2, 2012 at 0:38 | comment | added | Richard Stanley | For the generalization to commuting $k$-tuples of elements in $S_n$ and related results, see Exercise 5.13 in Enumerative Combinatorics, vol. 2. | |
| Sep 29, 2012 at 2:28 | history | edited | Geoff Robinson | CC BY-SA 3.0 |
Noted answer to more general version of the question
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| Sep 23, 2012 at 18:10 | comment | added | Mark Wildon | For symmetric groups there is the beautiful identity $$ \prod_{j=1}^\infty (1-u^j)^{-\sigma(j)} = \sum_{n=1}^\infty \frac{T(n)}{n!} u^n $$ where $T(n)$ is the number of triples of commuting elements in the symmetric group $S_n$ and $\sigma$ is the sum of divisors function. See arxiv.org/abs/1203.5079 by John Britnell for an elementary proof. | |
| Sep 23, 2012 at 16:15 | history | edited | Geoff Robinson | CC BY-SA 3.0 |
Noted equivalent formulation
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| Sep 23, 2012 at 15:48 | history | answered | Geoff Robinson | CC BY-SA 3.0 |