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2d
comment A Step in the proof of Rate of Convergence of Steepest Descent in Nocedal's Numerical Optimization
You are missing a $\bigtriangledown$ in your expansion. Next compute the derivative. Then remember the definition of $\bigtriangledown f$ in the first paragraph.
Sep
16
comment The number of lattice points in d-dimensional ball
I think you need $d\ge 4$. The statement is definitely false for $d=1$ and $d=2$.
Sep
11
reviewed Approve suggested edit on Verify that the sets B and S are spanning sets for $\mathbb{R}^3$.
Sep
11
reviewed Approve suggested edit on Minimise total cost and count ways
Sep
9
comment Strange factorial identity
@Erik Thanks. This is not implicit in my bijection, however, it should not be hard to modify the argument to get it, I think (Don't quote me on that).
Aug
29
comment SQRTSORT from Vazirani's book on algorithms
You can do a bubble sort like operation on blocks of $\sqrt{n}/2$ to do it in $O(n)$ SQRTSORT calls.
Aug
22
comment About putting $n$ distinct balls into $n$ distinct boxes.
If you want it exactly, I think that you will end up with a complicated summation. If you want something tractable you can use that fact that the number of balls in a bin is approximately Poisson distributed with mean 1.
Aug
20
comment Number of groups containing at least 1 and at most k elements
Essentially each occurrence of "!*" can be represented as a domino. I am not sure of a reference, it is a standard combinatorial technique.
Aug
18
answered Number of groups containing at least 1 and at most k elements
Aug
14
comment Fastest way to find if a given number is prime
What size random number? The answers are different for 1 digit numbers and 1000 digit numbers. How certain do you want to be that it is prime?
Aug
13
revised Solve the “two trains and a fly” problem the hard way
added 5 characters in body
Aug
13
comment Solve the “two trains and a fly” problem the hard way
@david You're probably right.
Aug
13
answered Solve the “two trains and a fly” problem the hard way
Aug
10
comment permutation and combination advanced
@ratish Yet another variant on the active contest problem codechef.com/AUG14/problems/TSHIRTS . We'll give an example sometime after August 15. Please stop asking contest problems.
Aug
8
awarded  Yearling
Aug
7
comment How to count the $r$-tuples of subsets of $\{1,\dots,n\}$ that are cyclically disjoint?
For $r=1$ you are counting the number of subsets of $[n]$. For $r=2$ you are counting the number of ways you can distribute the elements of $[n]$ in three bins (the members of $S_1$, the members of set $S_2$, and the poor ignored leftovers. For $r=3$ you are placing the elements of $[n]$ in four bins. For $r=4$ this breaks down because an element can be a member of $S_1$ and $S_3$ or a member of $S_2$ and $S_4$. Perhaps you need more bins.
Aug
7
comment Question regarding combinatorics of resistance network.
From your image, you are still missing two diagrams for n=4 (the two different ways of making a 1ohm resistor with 4 1 ohm resistors).
Aug
7
comment Question regarding combinatorics of resistance network.
See also math.stackexchange.com/questions/14645/…
Aug
7
comment Question regarding combinatorics of resistance network.
Two questions. 1) How do you know the total resistances are distinct? 2) If I understand your construction correctly, you do not seem to be able to create two resistors in series in parallel with another two resistors in series. Can you?
Aug
6
awarded  Nice Answer