16,674 reputation
21866
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location Mexico City
age
visits member for 2 years, 6 months
seen 19 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.


20h
comment Bounds on the numbe of groups of degree n
Oh, I had never seen the power of the gold badge tag been laid down like that, it was pretty hardcore.
20h
comment Group theory, the squares of G
you already proved it is normal. When $N$ is normal $gNhN=ghN$
20h
comment Set of common representatives and pigeonhole principle in one problem
Oh I see. thank you very much.
20h
comment if $A$ and $B$ are subnormal, then $A\cap B$ is subnormal
Did I make a mistake?
22h
comment an example for an arbitrary graph $G$ with even vertices which $\forall S \in V(G) , |N(S)|\geq |S| $ but there is no complete matching .
yeah, odd cycles do the trick, but he wants a connected one.
1d
comment What is the largest $k$ such that $ \frac { k(abc) }{ a+b+c } \le \left( a+b \right) ^{ 2 }+\left( a+b+4c \right) ^{ 2 } $?
Are the values poditive real numbers, otherwise we can take one of teh values as zero and the left becomes zero.
1d
comment What is the largest $k$ such that $ \frac { k(abc) }{ a+b+c } \le \left( a+b \right) ^{ 2 }+\left( a+b+4c \right) ^{ 2 } $?
Also, what kind of variables do we have?
1d
comment What is the largest $k$ such that $ \frac { k(abc) }{ a+b+c } \le \left( a+b \right) ^{ 2 }+\left( a+b+4c \right) ^{ 2 } $?
is this really level 5?
1d
comment Set with distinct subset sums
Yeah, but the repeated elements are not in the generating set, so it doesn't matter.
1d
comment Triangle-free graph with 5 vertices
You can also apply turan's theorem and it follows directly.
1d
comment Triangle-free graph with 5 vertices
Well, you can simply apply turan's theorem and you get the triangle free graph on $n$ vertices with most edges is always the complete bipartite graph in which both parts have as close a number of vertices as possible.
1d
comment $x^2-y^2=2s$, s cannot be an odd integer
Oh, this solution is much better than mine. +1
1d
comment Triangle-free graph with 5 vertices
with $5$ vertices. If there is no restiction on the number of vertices you can find a bipartite graph with as many edges as desired.
1d
comment Triangle-free graph with 5 vertices
Oh, we thought of the same thing, they say poor minds think alike.
1d
comment Number of ways to arrange items
$f_k(n)$ are the same as the stirling numbers of the first kind
1d
comment Minimize total cost of one kilometer
Something is wrong, the cost per hour should always be over $100$. are you sure the cost per hour is $25$ when the speed is $25$?
1d
comment How to solve this kind of problem?
I solved it using integers, I think it becomes harder if we can only use naturals.
1d
comment Check if Sequence is Graphic: 8, 8, 7, 7, 6, 6, 4, 3, 2, 1, 1, 1
I mean, you should count the degrees in the graph to make sure, but I can't find more conclusive evidence it is graphic
1d
comment Check if Sequence is Graphic: 8, 8, 7, 7, 6, 6, 4, 3, 2, 1, 1, 1
Well, I counted the degrees in the graph in the solution and it is correct, are you sure you copied the sequence correctly?
1d
comment How to solve this kind of problem?
The number in the bottom right corner has to be $1,-1,11$ or $-11$