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location Oxford, United Kingdom
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visits member for 3 years, 4 months
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Apr
13
comment Fast checking that overdetermined polynomial system does not have a solution
Note that the 1st method is not exact, and the software mentioned does its work with the usual floating point numbers. Particularly if your integer coefficients will get long, this won't be very reliable. That is to say, that you will have to look inside your systems just to make sure the coefficients don't blow up.
Apr
4
comment Does a spherical building embeds in a building of type $A_n$?
well, I won't be surprised if this has been improved (perhaps even by Tits himself) - that's why I referred to the book that is more or less the state of the art.
Apr
3
comment Does a spherical building embeds in a building of type $A_n$?
there has been some work done for $F_4$ and $E_k$ along the same lines as for polar spaces, but I don't know how conclusive are the results. Certainly, when there is just one building, given a field (e.g. for finite fields), the answer is yes.
Apr
3
answered Does a spherical building embeds in a building of type $A_n$?
Apr
2
comment Does a spherical building embeds in a building of type $A_n$?
you probably need to restrict your $B$ somehow. There are very weird generalised quadrangles (and thus buildings of type $C_2$) known which aren't embeddable in projective spaces at all.
Apr
2
comment integrality of a linear program — binary equality constaints
any sufficiently generic $c$ will give optimal face consisting of just one vertex. How often your polyhedron will have this vertex being 0-1? This will not happen very often, for sure.
Apr
2
comment integrality of a linear program — binary equality constaints
Please qualify what exactly you mean by a 0-1 solution. The underlying polyhedron of the LP has an optimal face, say, $F$. Are you asking for a criterion for $F$ to contain a 0-1 vector? Something else?
Mar
31
comment In which fixed-point free representations is the sum of every 3 elements invertible?
OK, Geoff, I must say I was totally humbled by your reference to Clifford's theorem :-)
Mar
30
comment In which fixed-point free representations is the sum of every 3 elements invertible?
Why would 3 even divide $|G|$ ? And why must the normal 3-complement be Abelian?
Mar
30
comment In which fixed-point free representations is the sum of every 3 elements invertible?
you wrote "sum of every 3 elements", meaning "sum of every 2 elements and the identity"...
Mar
30
revised Which graphs generate a matroidal independence complex?
added 72 characters in body
Mar
30
comment Which graphs generate a matroidal independence complex?
I stand corrected.
Mar
29
answered Which graphs generate a matroidal independence complex?
Mar
29
reviewed Approve suggested edit on An inequality involving sums of powers
Mar
25
comment Counting extrema on a simplex
you certainly can write down the Lagrange conditions and use algebraic geometry to write down some bounds, but they won't be very useful: they would typically count complex as well as real solutions, and I bet you won't beat known results on number of maximal independent sets in graphs this way. See arxiv.org/abs/1104.1243
Mar
25
answered Counting extrema on a simplex
Mar
25
comment Independence Number of K4-free planar graphs
OK, I was thinking about the maximum ratio, sorry.
Mar
24
comment Independence Number of K4-free planar graphs
IMHO it gets nontrivial if you request the graph to be 3-connected, as well.
Mar
24
comment Independence Number of K4-free planar graphs
Do you want to restrict to connected graphs? Otherwise, a bunch of non-connected vertices is as best as you can hope for.
Mar
24
reviewed Approve suggested edit on Is the countable intersection of residual sets in [0,1] with Hausdorff dimension 1 of full Hausdorff dimension?