bio | website | cs.ox.ac.uk/people/… |
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location | Oxford, United Kingdom | |
age | 50 | |
visits | member for | 3 years, 4 months |
seen | 7 mins ago | |
stats | profile views | 1,597 |
Mar 23 |
reviewed | Approve suggested edit on Holomorphic vector field on Fano Kählerâ€“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 |