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seen Oct 7 at 3:02

Apr
19
comment How to transform matrix to this form by unitary transformation?
Thanks! Will unitary transformation keeps the spectral radius?
Apr
2
comment Is there such a matrix in $SO(n)$?
@მამუკაჯიბლაძე I give an example for $n=2$ in a Mathematica file(click the link please)
Apr
2
comment Is there such a matrix in $SO(n)$?
@მამუკაჯიბლაძე Thanks for your comment! Note that $a'_i, b'_i$ may be un-normalized.
Mar
25
comment making a graph well-covered without changing its Shannon capacity
The new one added vertex should be adjacency with each vertex which can be in a maximum independent set at least.
Jan
15
awarded  Peer Pressure
Jan
15
comment Lovász function of the Möbius ladder
Since the Möbius ladder is isomorphic to the circulant graph $Ci_{2n}(1,n)$, we can think about $Ci_{2n}(1,n)$. But I have no idea too.
Oct
29
awarded  Scholar
Oct
29
accepted What is the maximum of the ratio $\vartheta(G)/\alpha(G)$?
Oct
29
comment What is the maximum of the ratio $\vartheta(G)/\alpha(G)$?
Thanks so much Casteels! You're so kindly focus on this question.
Oct
28
revised What is the maximum of the ratio $\vartheta(G)/\alpha(G)$?
edited tags
Oct
28
comment What is the maximum of the ratio $\vartheta(G)/\alpha(G)$?
Thanks so much! Here is a similar question shows $log_2(q)+3/2$ will not be the right size.
Oct
27
awarded  Supporter
Oct
27
comment What is the maximum of the ratio $\vartheta(G)/\alpha(G)$?
Thanks! Your answer is very helpful! I also considered Payley graphs, but it is not adequate to say the upper bound is infinity because the numerical result shows the maximum is $5.4$ for $q<9973$. Is there some other pattern of graphs whose $ϑ(G),α(G)$ are all known? Thanks again!
Oct
27
revised What is the maximum of the ratio $\vartheta(G)/\alpha(G)$?
deleted 1 characters in body
Oct
27
asked What is the maximum of the ratio $\vartheta(G)/\alpha(G)$?
Sep
25
comment How to transform matrix to this form by unitary transformation?
Thanks! Your answer is so helpful! May you kindly talk about why you choose the case where $(m_i) = (65, 72, 25, 69, 2)$ and which software do you use?
Aug
24
awarded  Commentator
Aug
24
comment Nontransitive dice: the least number of faces?
@WillSawin It is a cool idea! We can always to do this perturbation, but the nontransitivity is only related to the order of the numbers but not what they exactly are.
Aug
23
comment Nontransitive dice: the least number of faces?
@WillSawin Yeah $n$ is the number of dice.
Aug
23
comment Nontransitive dice: the least number of faces?
$m=3$ for $n=3$, for example, the three dices are {1,5,9}, {2,6,7},{3,4,8}.