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Results tagged with big-list
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user 58345
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
15
votes
When is 2 qualitatively different from 3?
Due to the Poincaré–Bendixson theorem, continuous dynamical systems can not be chaotic in two dimensions, while they can in three dimensions.
13
votes
When is 2 qualitatively different from 3?
In a three or higher dimensional Euclidian space, the infinitesimal conformal transformations generate a finite dimensional Lie algebra, while in two dimensional Euclidian space, it is an infinite dim …
8
votes
When is 2 qualitatively different from 3?
If we say that integer partitions correspond to $n=1$, plane partitions to $n=2$ and solid partitions to $n=3$, then the cases $n=1,2$ are special in the sense that a simple generating function is kno …
48
votes
When is 2 qualitatively different from 3?
Fermat's last theorem states that there are no non-trivial integer solutions to $x^n+y^n=z^n$ for $n=3$ (or in fact any $n\geq 3$), but there are of course many Pythagorean triples that give solutions …
10
votes
Listing applications of the SVD
In quantum physics, one often studies the entanglement between to parts of the system, in terms of the entanglement entropy, which can be expressed in terms of the Schmidt coefficients occurring in th …
5
votes
Important formulas in combinatorics
The Durfee square formula for the generating function of the number of partitions doesn't seem to be in this list yet, I find it rather appealing:
$$
\frac{1}{(q)_\infty} = \sum_{n\geq 0} \frac{q^{n^2 …