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Results tagged with gm.general-mathematics
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user 9025
Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
2
votes
Accepted
Multivariate expansion in terms of single variate products: what is the name for this?
This paper calls it "separable of rank $n$" if $n$ is the number of terms in the sum. If the sum is an infinite one, the condition is very weak (for example it includes all functions with a convergen …
- 37.7k
-1
votes
Asymptotics of a function
$f(n) = n^n 4^{-4n} (1 + O(n^{-4}))$. The sum is strongly dominated by its last term. I hope this isn't homework.
Apologies. I misread the question exact as Benoît suggests.
- 37.7k
1
vote
Find the expansion of the exact solution (beyond Taylor)
Only the assumption $S\to\infty$ is needed to verify that there is a local minimum near the place where $V_-$ has its minimum, namely at $\mu=\mu_0 = 12^{1/6} S^{-2/3}$, but it doesn't give the approx …
- 37.7k
2
votes
17 camels trick
A simple graph theory example in the spirit of the question.
THM. Let $G$ be a connected graph with $2j$ vertices of odd degree. Then there are $j$ (open) eulerian trails whose endpoints are the ver …
26
votes
Accepted
Formal writing: numbers under 10
Generally speaking you should try to distinguish between an English number and a mathematical number. As in "Over the next five chapters we will prove that 5 is a prime number." Never spell out a num …
- 37.7k
5
votes
Structures that turn out to exhibit a symmetry even though their definition doesn't
In the definition of "Latin square" there is complete symmetry between the roles of "row", "column" and "symbol", so that any of the 6 permutations of that role produces another Latin square.
10
votes
Computationally challenging integer sequences
Here is a sequence that is quite famous but not in OEIS I think (perhaps because too few elements are known). A hypergraph is $v$-uniform if every edge has $v$ vertices, and 2-colourable if the verti …
- 37.7k
23
votes
Mathematical habits of thought and action which would be of use to non-mathematicians
This is a sort of anti-answer. When the Unabomber Manifesto was published by the NYT, someone in sci.math (or sci.math.research) recognised the reasoning as being like that of a mathematician. I don' …
7
votes
Frequency of papers showing academic misconduct among the articles indexed by MathSciNet and...
What you should do about it: (1) Decide if the case is blatant enough that action is demanded. There are many borderline cases where a previous paper is attributed but not adequately; probably they ar …