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5h
answered functions representable as a sum of two permutations
7h
answered The non-uniform probability of sums from the throw of multiple dice
9h
comment How to find the value of $2g(1)+2f(1)-h(1)$?
The continuity of $f$ seems to be irrelevant, since only $f(1)$ figures in the problem?
9h
comment Orthonormal Basis of $L^2$
The lower limit in the sum in the first displayed equation should be $0$, not $-\infty$?
9h
revised Is there a special name for functors from a category C to a subcategory of C?
edited tags
9h
comment Permutations for a set of rules
@archit: Yes, you should, and I'll be happy to try to answer it :-)
13h
comment To solve $n(n+1)(n+2)=6m^3$ in positive integers $m,n$
@TonyK: I hadn't known it either; I came across it looking for what's known on diophantine approximations of $\sqrt[3]2$. Another interesting paper I found was Rational approximations to $\sqrt[3]2$ and other algebraic numbers revisited by Paul M. Voutier (Journal de Théorie des Nombres de Bordeaux 19 (2007), 263–288), which gives the bound $$\left|2^{1/3}-\frac pq\right|\gt\frac{0.25}{\left|q\right|^{2.4325}}$$ for integers $p$, $q$ with $q\neq0$, which I suspect could also be used to resolve the present question.
13h
comment To solve $n(n+1)(n+2)=6m^3$ in positive integers $m,n$
P.S.: I see now that the paper I cited actually gives references (Delone 1922, Nagell 1925) that had proved the paper's result for $n=3$ long ago.
13h
answered To solve $n(n+1)(n+2)=6m^3$ in positive integers $m,n$
14h
comment To solve $n(n+1)(n+2)=6m^3$ in positive integers $m,n$
That statement on Wikipedia was introduced in 2007 by this edit, which was rather inappropriately marked as "minor". No source is given in the edit summary. The user who added the statement was active on Wikipedia for 12 days and hasn't contributed since. I wouldn't put too much stock in that statement. (Also I'd expect that if this were known it would be recorded in the OEIS sequence of the tetrahedral numbers, which notes the three solutions in the square case.)
15h
comment To solve $n(n+1)(n+2)=6m^3$ in positive integers $m,n$
A numerical check finds no small non-trivial solutions.
15h
comment Inverse of the complex exponential function, considered as a multivariable function
Yes, that's right.
16h
comment To find positive integers $n$ such that $\dfrac {n(n+1)(n+2)}6$ is a perfect square
@Pjotr5: This is a complete answer; if you post it as an answer, the question can be marked as answered.
16h
comment Number of permutations on nearest neighbors
You may want to look into the literature on packed loop models. The sort of permutation that you describe is associated with a graph on $A$ in which the cycles of the permutation are loops consisting of links between nearest neighbours, and such loop configurations have been extensively studied in theoretical physics.
17h
comment Is there a way to figure out the number of possible combinations in a given total using specific units
@AndrewMartin: That question I linked to might be of help; otherwise feel free to come back and ask :-)
17h
comment Permutations for a set of rules
@archit: Sorry, I had a mistake in part (a); I hadn't taken into account that the other five trains can do what they want while the first one waits; I corrected that. By "weak" I just mean that it's not that much of a constraint, that it's hard to violate because one train has to wait for the entire available time in order to violate it. (I've changed it to "rather weak" because it turned out to be a bit stronger than I first realized. :-)
17h
revised Permutations for a set of rules
corrected mistake in part a)
18h
answered Is there a way to figure out the number of possible combinations in a given total using specific units
18h
answered How to “see at a glance” the solution to the exercise “Show that $\langle (1,2,3… n),(1,2,3… m)\rangle$ contains a 3 cycle, if $1 < n < m$”?
18h
answered Number of representatives from states to from a comittee?