5,271 reputation
929
bio website cs.ox.ac.uk/people/…
location Oxford, United Kingdom
age 51
visits member for 4 years, 6 months
seen 21 hours ago

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.