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Feb
17
reviewed Close Grandi's series contradiction
Feb
13
comment Little O Bound, Combinatorics
You're asking us to read your mind. What's the property $S_k$?
Feb
11
comment i^i^i^i^… Is there a pattern?
@nayrb, since $(a^b)^c = a^{(bc)}$, the convention is that $a^{b^c} = a^{(b^c)}$.
Feb
11
comment Logic behind the ID checksum?
@Prakhar, it's one of the first things I do when trying to understand a mystery sequence of numbers. It's a good way of identifying polynomials (if you repeat the operation $n$ times then an order-$n$ polynomial will give a constant vector).
Feb
11
comment Logic behind the ID checksum?
@Prakhar, "take first differences" means taking each adjacent pair and subtracting one from the other. So $1 - 2 \equiv 10, 6 - 1 \equiv 5, 3 - 6 \equiv 8, \ldots$.
Feb
11
answered Logic behind the ID checksum?
Feb
9
comment Combinatorics - falling ball through a labyrinth
And for $m \times n$ labyrinths it's $\binom{m+n}{m}$, being a simple manifestation of staircase walks.
Feb
4
comment Proving that a language is not context-free
I suggest using the pumping lemma to derive a contradiction. That's the way pumping lemmas are typically used to prove that languages don't fall into the relevant class.
Feb
4
comment Which are the most effective modern intuitive definitions of a vector?
@twirlobite, "direction" is a very ineffective intuition. It makes sense in Cartesian products over fields of characteristic zero, but what would it mean in vector spaces over fields of finite characteristic?
Feb
3
answered Gossip problem why 4?
Jan
25
comment Find three $10\times10$ orthogonal Latin squares.
What's the link to Latin squares?
Jan
25
revised Proof of a Known Claim About Languages
added 489 characters in body
Jan
25
answered Proof of a Known Claim About Languages
Jan
25
comment Proof of a Known Claim About Languages
@xavierm02, $a \notin \{ab\} \implies a \in \overline{\{ab\}} \implies a \in (\overline{\{ab\}})^*$
Jan
25
comment Proof of a Known Claim About Languages
@xavierm02, $a \in (\overline{ab})^*$.
Jan
25
revised Proof of a Known Claim About Languages
added 95 characters in body
Jan
24
comment Consider the smallest number in each of the $n\choose r$ subsets (of size $r$) of $S=\{1,2,\ldots,n\}$…
This might be clearer if you parameterise $\mu$.
Jan
16
comment enumerating in pseudo random order
I think that your amended explanation corresponds to a series of permutation compositions such that if we view the counter $x$ as having digits base 4 of $abcd$ then $$f(x) = (2301)^a A (2301)^b B (2301)^c C (2301)^d D$$ and that you want to ensure that all possible permutations are generated in an order which passes some kind of pseudorandomness test. Does this seem about right?
Jan
15
comment enumerating in pseudo random order
You seem to be trying to find $n^n$ distinct permutations of $n$ items, which is impossible for $n > 1$. Have I misunderstood something?
Jan
15
comment Can 18 consecutive integers be separated into two groups,such that their product is equal?
Although note that Erdős doesn't actually prove it for products of fewer than 100 consecutive numbers: he just refers to a paper by Seimatsu Narumi, Tôhoku Math. Journal, 11 (1917), 128-142 which apparently proves cases up to 202 consecutive numbers by special arguments.