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21760
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location Monkey Island, OK
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visits member for 2 years, 4 months
seen 4 hours ago

Hello, I am a freshman at The National Autonomous University of Mexico (UNAM).

My interests are contest problems,elementary number theory, combinatorics, graph theory, linear algebra, group theory, abstract algebra and I have been meaning to learn category theory and matroids.


2d
comment Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$?
Hmm, there are various proofs of the replacement theorem, I shall write one down
2d
comment Find maximum number of nodes in a regular graph of degree 4 and diameter 2
A rather poor upper bound is $21$ since every vertex can reach at most $4$ vertices and each of those at most $4$, so $1+4+16$ is an upper bound, but I am pretty sure it isn't sharp
2d
comment Prove that $ |A∪B|=|A|+|B|-|A∩B|$
Well, I guess this question wouldn't be considered valid in a rigorous math context either.
2d
comment A complicated question
excelent title selection!
2d
comment Prove that $ |A∪B|=|A|+|B|-|A∩B|$
What is an informal proof?
2d
comment Normalizer and centralizer are equivalent when $p$ is the smallest prime dividing $|G|$
Where did you find this problem?
Oct
19
comment Set of numbers which can not be represent as $a_1^n+a_2^n+…a_n^n$
Interesting question, I would say it is infinite for all $n\geq 2$
Oct
19
comment Math for Computer Science
glad I could help
Oct
19
comment $H\trianglelefteq A$ and $K\trianglelefteq B\Rightarrow HK\trianglelefteq AB$?
In other words, if this was true all subgroups would be norma
Oct
18
comment Stuck with modular arithmetic problem using multiplication property
what you did was right, but you're assuming you have an if and only if. clearly $3n$ is always $0$ mod 3, so you can't conclude absolutely anything about $n$ from that fact
Oct
18
comment Probability of getting 3 cards in the same suit from a deck
you're very welcome, glad I could help
Oct
18
comment Probability of getting 3 cards in the same suit from a deck
It is what is called a binomial coefficient In some schools they write is as $12C3$ instead of $\binom{12}{3}$ In the calculator it is the button that has a symbol $nCm$. $\binom{12}{3}$ is the number of subsets of three elements a set of $12$ elements has. It is also said to be the number of ways to select three things out of 12 options when the order "doesn't matter"
Oct
18
comment Prove or disprove if $G$ is 2-edge-connected then there exist 2 edges disjoint $u-v$ trail such that every edge of $G$ lies on one of these trails.
Hmm, that's actually right, I somehow forgot that they need to be $u-v$ trails, it seems it can be done with one, but not with two, and the reason you give sounds sound.
Oct
18
comment Prove or disprove if $G$ is 2-edge-connected then there exist 2 edges disjoint $u-v$ trail such that every edge of $G$ lies on one of these trails.
2-edge connected implies connected. All you need is connected with exactly $2$ odd vertices so it has an eulerian path.
Oct
18
comment Prove or disprove if $G$ is 2-edge-connected then there exist 2 edges disjoint $u-v$ trail such that every edge of $G$ lies on one of these trails.
are you sure there are only $2$ odd vertices?
Oct
17
comment What does a day in the life of a mathematician look like?
hahaha, that second to last sentence killed me
Oct
17
comment $H\leq G$ implies $H^{'}\leq G^{'}$?
That book is awesome, I'm working through it also!
Oct
17
comment $H\leq G$ implies $H^{'}\leq G^{'}$?
woops, thank you Timbuc. Fixed.
Oct
17
comment Sets of size at least $k$ with intersection of size at most $1$ cool problem.
hmm, I did that and didn't think of bounding the degrees. Sometimes I dismiss ideas on the account they don't seem "strong enough". Thanks a lot though.
Oct
17
comment Sets of size at least $k$ with intersection of size at most $1$ cool problem.
wow, how are you so good at this type of problems, it isn't the first time I've seen you do this.