963 reputation
1418
bio website mathoverflow.net/users/19885/…
location Between Two Moments
age
visits member for 3 years
seen Dec 18 at 10:37

$T$. $S$. $Eliot$, Introduction to Dante's Inferno: " Hell is a place where nothing connects with nothing. "

$Johann$ $von$ $Neumann$: " In mathematics you don't understand things, You just get used to them. "

$A$. $A$. $Zinoviev$: " Where there are problems, there is life. "

$P$. $R$. $Halmos$: "I do believe that problems are the heart of mathematics, and I hope that as teachers, in the classroom, in seminars, and in the books and articles we write, we will emphasize them more and more, and that we will train our students to be better problem-posers and problem-solvers than we are. "

$Shahrooz$: " Physics is mirror front of universe, but mathematics is the rules of reflection. "


Dec
18
comment Open problems with monetary rewards
Dear Voloch, I think you are right. But it is a little strange for me, why mathematicians should forget the heritage of the great mathematician like MacWiliams? It is just $10$ dollar, and I think someone must accept it and pay it in the future. If I can pay, I will accept it, maybe a good news.
Dec
17
answered Open problems with monetary rewards
Dec
11
awarded  Yearling
Nov
14
awarded  Nice Answer
Nov
5
answered Math books for advanced high school students
Sep
16
revised Non-DS circulant graphs
added 337 characters in body
Sep
16
comment Non-DS circulant graphs
In general, the answer is no, even for special type of graphs.
Sep
16
answered Non-DS circulant graphs
Aug
25
answered Largest eigenvalue adjacency matrix-link deletion
Aug
14
comment For integers $a \ge b > 1$ is $f(a,b) = a^b + b^a$ injective?
Since nobody answered the question until now (after 8 vote), it seems that it is hard. But where am I wrong? Let $a=b+x$, so for every fixed $b$, the function $f_b(x)=(b+x)^b+b^{b+x}$ is increasing in variable $x$. So induction on $b$ must solve the problem.
Aug
13
revised Cospectrality and dimension of graphs
Corrected a mistake
Aug
12
answered Cospectrality and dimension of graphs
Aug
10
comment Do runs of every length occur in this sequence?
@r.e.s- About existence of the limit, you are right. I just talked approximately, but I believe that this limit is so close to $\frac{1}{2}$, even if it is irrational. For your second comment, it was just an optimistic view to convert the problem to bit-wise case (against half-block adding). In that case, the probability that $i$-th position be $1$ must increase for sufficiently large $i$ and it increases the probability of seeing a repeated $1$ sequence. This problem is like a phylogeny in genetics. What is the application of this nice problem?
Aug
9
comment Do runs of every length occur in this sequence?
One vote and also favorating question. It seems that the behaviour of consequtive 1 in this squence is more chaotic. This is just a view: let $a_n$ and $L_n$ denote the number of ones and total length of sequnces in the $n$-th iteration, respectively. So (if I do not be wrong), $a_n\thickapprox‎ \frac{3}{2}a_{n-1}$ and $L_n \thickapprox 2(3/2)^n‎$. Now, $\frac{a_n}{L_n}$ tends to $\frac{1}{2}$, when $n$ goes to infinity. So, I think the conjecture is true, but its proof must be difficult, because of $\frac{1}{2}$.
Jul
27
accepted irreducible polynomials on the polynomial sequence
Jul
15
comment irreducible polynomials on the polynomial sequence
@David, the second question let us to choose carefully the $g_i(x)$, such that $P(x,y)$ generates infinite irreducible polynomial. It is a special case such that we know the conjecture is true for it. Anyway, thanks for your answer.
Jul
14
asked irreducible polynomials on the polynomial sequence
Jun
11
awarded  Popular Question
May
22
answered Examples of graph properties characterized by forbidden (not necessarily induced) subgraphs
Jan
31
awarded  Popular Question