bio | website | cs.ox.ac.uk/people/… |
---|---|---|
location | Oxford, United Kingdom | |
age | 51 | |
visits | member for | 4 years, 6 months |
seen | 21 hours ago | |
stats | profile views | 2,255 |
Apr 28 |
reviewed | Close Algebraic Groups of Type H_3 and H_4 |
Apr 28 |
reviewed | Close Backward Uniqueness for the wave equation |
Apr 28 |
reviewed | Close What defines a “short proof”? |
Apr 28 |
reviewed | Leave Open Good ways to organize old personal mathematical resources |
Apr 28 |
reviewed | Approve Is the set $ AA+A $ always at least as large as $ A+A $? |
Apr 27 |
comment |
Complexity :: Integer Programming :: Non-Poly Example
an example in this area is something that depends on a parameter; say, an array of length $n$ of integer numbers, and the task is to sort them; or a graph on $n$ vertices, and the task is to find a maximum clique. See, it's crucial that there is $n$ involved, because the question computational complexity answers is "provide a function of $n$ that tells the number of operations needed to solve the task". |
Apr 27 |
comment |
Complexity :: Integer Programming :: Non-Poly Example
the notions of NP-completeness and polynomial-time solvability are about classes of problems, and not individual examples. |
Apr 27 |
reviewed | Close Is there a nonzero sheaf with all cohomologies vanish? |
Apr 27 |
comment |
Mysterious identity between numbers of odd/even meander systems
I bet this is a relatively easy exercise with generating functions; a one Richard Stanley can do in his head :-) |
Apr 27 |
comment |
Mysterious identity between numbers of odd/even meander systems
So, do you have explicit formulae for $OMS$ and $EMS$, or not? |
Apr 27 |
comment |
Mysterious identity between numbers of odd/even meander systems
then what kind of "explicit expressions" are you talking about? |
Apr 27 |
comment |
Mysterious identity between numbers of odd/even meander systems
Then why do you ask "whether this is true"? So the numbers are the same, as you just said. Do you rather ask for an explicit bijection? |
Apr 27 |
comment |
Mysterious identity between numbers of odd/even meander systems
Did you try putting your numbers into oeis.org and see what it tells you? |
Apr 26 |
reviewed | Close Do those manifolds atrached to L-functions give rise naturally to motives? |
Apr 26 |
answered | Computionally efficient vertex enumeration for (convex) polytopes |
Apr 26 |
reviewed | Leave Closed Maximality statements that cannot be proved using $\mathsf{ZL}$ |
Apr 25 |
comment |
Is anything known about the eigenspectrum of the regular representation of the permutation group?
@QiaochuYuan - right, I missed this point. |
Apr 25 |
comment |
Is anything known about the eigenspectrum of the regular representation of the permutation group?
@QiaochuYuan - the behaviour of a permutation matrix is not determined by the order alone; it is determined by the cyclic structure of the permutation. E.g. the multiplicity of eigenvalue 1 is the number of cycles. |
Apr 25 |
comment |
Is anything known about the eigenspectrum of the regular representation of the permutation group?
a similar argument works for elements of order 3; as an eigenvalue $\lambda$ and its conjugate must occur with the same multiplicity, we see that the number of eigenvalues equal to 1 must be equal to twice the number of eigenvalues $\zeta$, for $\zeta$ a fixed primitive cubic root of unity. |
Apr 25 |
comment |
Is anything known about the eigenspectrum of the regular representation of the permutation group?
for the elements of order 2, it's trivial that the number of eigenvalues equal to 1 equals the number of eigenvalues equal to -1, as the trace of each non-identity element equals to 0. |