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Aug
20
comment I'm a late-bloomer, apparently. Do I have any hope of college?
Absolutely not too late. 26 is young. I know a middle-aged woman who went to college knowing virtually no math. She started with the very lowest level course on offer at the community college, which was basic arithmetic. She went on to do calculus, differential equations, linear algebra etc.
Aug
16
comment What is a cycle hypergraph?
It's been my experience that hypergraph terminology isn't very standardized, so I would check with individual references.
Aug
15
comment Is “random variable” really random?
It's not random, but it models randomness.
Aug
13
comment Chidzalo's Sequence
+1 for "Chizalo's sequence" :)
Aug
13
comment How many anagrams of a given word exists with constraints
You could use the Goulden-Jackson cluster method. This allows you to enumerate words that avoid any collection of substrings. This loses a lot of the structure of the problem, though, since you would just use the substrings MIS, ISS, etc. and forgetting where they come from. It would also get hairy pretty quickly if the word length $n$ was long as it would solving $n \times n$ systems of equations.
Aug
13
comment Counting number of times a given segment will occur in all subarrays
This is not very clear. Can you explain what you mean by subarray, and what it means for a segment to occur in a subarray? I don't see why $[1,2]$ "occurs in" $\{23,5\}$.
Aug
13
comment What is the name of the transform which finds the number of ways to make partitions of the given sizes?
Sure, no problem. If your sequence is finite then $f(x)$ will be a rational generating function, and then the coefficients will satisfy a recurrence relation that makes them easy to compute. I'm not sure what the fastest way to compute them would be if the sequence is infinite.
Aug
13
answered What is the name of the transform which finds the number of ways to make partitions of the given sizes?
Aug
12
comment Counting the size of the largest sets of independent strings
For an upper bound, perhaps a pigeonhole principle argument would work.
Aug
12
comment Counting the size of the largest sets of independent strings
Perhaps the probabilistic method would be useful here. That is, choose $k$ strings uniformly at random and try to show that the probability of having no strings match is $>0$. This would give you a lower bound of $k$.
Aug
12
comment Is there a “greater than about” symbol?
This symbol is not very common in my experience, so I would be careful to explain what you mean by it.
Jul
30
comment Finding math research problems
There has to be a reason you're interested in math - so do that! You don't necessarily have to wait for somebody to hand you an open problem. There's something in the mathematical universe that interests you. So hone in on that, focus your interest, and if you can't find a problem from somebody else, you can always make up your own.
Jul
29
comment Of strings and substrings: A problem of probability
The "Goulden-Jackson cluster method" is a sort of calculus for counting words according to occurrences of subwords that might be useful. See my answer here.
Jul
27
answered Find the total number of matchings in a complete graph with even vertices
Jul
25
comment An approach to approximating the harmonic series.
I'm not sure what you mean. You might be interested in the digamma function $\psi(x)$ that satisfies $\psi(x+1) - \psi(x) = 1/x$.
Jul
25
comment An approach to approximating the harmonic series.
See: en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant :)
Jul
22
comment Article writing: How to represent a matrix by its elements?
I would use $a_{ij}$ or $a_{i,j}$. The dimensions should be pretty clear from the context, although your notation would be fine too.
Jul
17
comment Online publication of short essays
Sounds like a good blog post to me.
Jul
14
comment On the value of proofs vs counterexamples
You could disprove a statement that way, but ultimately any proof is logically equivalent to showing that there exists a counterexample, since that's what it means for such a statement to be false. So either you can trace through the logic of the proof and discover that you essentially found a counterexample in disguise, or else it's really a nonconstructive proof.
Jul
14
comment Notation for “set of leaves of a tree” when leaves are “repeated”
I would just say each leaf is labeled with any arbitrary number rather than saying that the leaves are repeated, although you might be able to get away with that if the context is clear.