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bio website cs.ox.ac.uk/people/…
location Oxford, United Kingdom
age 50
visits member for 3 years, 4 months
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Mar
23
reviewed Approve suggested edit on Holomorphic vector field on Fano Kähler–Einstein manifold
Mar
17
answered Determine if a graph has a large clique
Mar
10
comment Is the domination number of a combinatorial design determined by the design parameters?
for 3-dimensional projective spaces $PG(3,q)$ and their hyperplane designs, probably the best one can do is $\gamma=2(q+1)$: take the points and the hyperplanes on a line.
Mar
10
comment Is the domination number of a combinatorial design determined by the design parameters?
OK, I see: take a line $\ell_0$ and a point $p_0\in\ell_0$. Then set $P$ to be the points of $\ell_0$ except $p_0$ and $L$ to be the lines on $p_0$ except $\ell_0$. Nice :-)
Mar
10
comment Is the domination number of a combinatorial design determined by the design parameters?
A dominating set in this case is a subset $(P,L)$ of points and lines such that each line on the plane not in $L$ intersects $P$ and each point of the plane not in $P$ lies on some $\ell\in L$, right? I see how $\gamma=2q$ works for $q=2$, but for bigger values, I don't...
Mar
9
comment Is the domination number of a combinatorial design determined by the design parameters?
Hmm, for $q=2$ this gives $\gamma=2$. This cannot be right, as the size of the set of neighbours of such a set is at most 6, but the graph has 14 vertices.
Mar
9
comment Is the domination number of a combinatorial design determined by the design parameters?
What is the value of $\gamma$ for a projective plane of order $q$?
Mar
9
comment Is the domination number of a combinatorial design determined by the design parameters?
GAP package Design can apparently produce such a list for you, see gap-system.org/Manuals/pkg/design/htm/CHAP007.htm
Mar
6
comment Estimating a sum involving binomial coefficients [refined]
Your sum is certainly hypergeometric too, but it is the ordinary, aka Gaussian, one, i.e. $ _2F_1(q-m, q-m; -m; -1)$, (if I got it right), and there is a lot of stuff known about them, e.g. explicit integral representations. Should be routine to compute an asymptotic using the latter.
Feb
26
revised Estimating a sum involving binomial coefficients [refined]
fixed computational error
Feb
26
comment Estimating a sum involving binomial coefficients [refined]
see my edit in the answer
Feb
26
revised Estimating a sum involving binomial coefficients [refined]
added an explanation
Feb
25
comment Algorithms to compute largest gap between smallest nonzero eigenvalues of sparse symmetric matrix
I never heard of software specifically for computing gaps, but computing $k$ minimal consecutive eigenvalues is well-known how to do for sparse matrices, see e.g. caam.rice.edu/software/ARPACK (ARPACK has interfaces to Python and Matlab, so you don't have to program in Fortran to use it)
Feb
25
comment Software for noncommutative Groebner bases over rational function fields
perhaps Singular can do it? You might want to check it out: singular.uni-kl.de
Feb
25
revised Algorithms to compute largest gap between smallest nonzero eigenvalues of sparse symmetric matrix
added dollars
Feb
25
answered Estimating a sum involving binomial coefficients [refined]
Feb
24
comment Generators of cyclic group of finite fields
What do you mean by "explicitly" finding $a$? No, I don't think there is some magic formula for it; one needs to do computations, generally speaking. There is a special class of irreducible polynomials, called primitive, for which any root has maximal period. Again, there is no generally known formula how to find such polynomials.
Feb
17
awarded  Custodian
Feb
17
reviewed Approve suggested edit on Pushouts in the category of adjunctions
Feb
17
revised Is there a theory of oriented subspace arrangements?
added the 0,1,-1 weights discussion, fixed a typo