bio | website | cs.ox.ac.uk/people/… |
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location | Oxford, United Kingdom | |
age | 50 | |
visits | member for | 3 years, 8 months |
seen | 17 hours ago | |
stats | profile views | 1,719 |
Jul 16 |
comment |
Orthogonal Groups over finite fields
Geoff, thanks, I stand corrected. I've removed the wrong comment. I'll dig the stuff on spinor norm up when/if I get to teach graduate group theory :–) |
Jul 15 |
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Generating set of orthogonal matrix
In even characteristic the set of invertible $A$ s.t. $AJA^\top=J$ would give you the symplectic group rather than an orthogonal group. |
Jul 15 |
revised |
Orthogonal Groups over finite fields
an example added |
Jul 14 |
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Orthogonal Groups over finite fields
en.wikipedia.org/wiki/Orthogonal_group#The_Dickson_invariant says "Dickson invariant can be defined as D(f)= rank (I-f) modulo 2, where I is the identity (Taylor 1992, Theorem 11.43). Over fields that are not of characteristic 2 it is equivalent to the determinant: the determinant is −1 to the power of the Dickson invariant." I don't know. At least I am glad that I wrote "(sometimes you might have to take the commutator subgroup)" in my answer. :–) |
Jul 14 |
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Orthogonal Groups over finite fields
according to Wikipedia, Dickson invariant only matters in even characteristic. In odd characteristic it cuts out the same normal subgroup as the determinant. |
Jul 14 |
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Orthogonal Groups over finite fields
Geoff, are you saying that for $p$ even one actually would have an index 2 subgroup regardless, as $SO^+_{2n}(p)=O^+{2n}(p)=D_n(p)$ in this case, but one still has nontrivial Dickson invariant? Then, oops, my last comment is only true for $p$ odd. As a lame excuse I can only say that my copy of the Atlas is in the office :–) |
Jul 14 |
answered | Orthogonal Groups over finite fields |
Jul 13 |
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Mclaughlin Graph
By the way, while it's well known that McLaughlin graph is characterized by its parameters, I'm much less sure about the second graph in question. |
Jul 12 |
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Mclaughlin Graph
edited tags |
Jul 12 |
answered | Mclaughlin Graph |
Jul 11 |
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What is the effect of adding one edge on the number of spanning trees of a given graph ?
you might want to look at various versions of Weighted Matrix Tree Thm, see e.g. math.uwaterloo.ca/~dgwagner/Networks.pdf |
Jul 9 |
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Lower bound of the size of a collection of subsets with a intersecting property
$C_n^{n/2}$ is old notation still common in some countries... |
Jul 9 |
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Lower bound of the size of a collection of subsets with a intersecting property
I guess $C_n^{n/2}$ denotes $\binom{n}{n/2}$. |
Jul 8 |
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$\ell_o$ Minimization (Minimizing the support of a vector)
Sorry, what do you denote by $\|\dot\|_0$? |
Jul 7 |
revised |
The chromatic number of a Hamming-related graph
edited tags |
Jul 7 |
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The chromatic number of a Hamming-related graph
I've added above a explanation about Delsarte / Lovasz bounds. If I see this right, the number of variables in the underlying linear program is something like $n-k+1$, so for $k$ very close to $n$ one might have a fighting chance to get something out of this. |
Jul 7 |
revised |
The chromatic number of a Hamming-related graph
added 1255 characters in body |
Jul 7 |
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The chromatic number of a Hamming-related graph
I rewrote my answer so that it makes sense (hopefully). |
Jul 7 |
revised |
The chromatic number of a Hamming-related graph
added 631 characters in body |
Jul 7 |
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The chromatic number of a Hamming-related graph
you are right, I didn't think straight here :) What I meant to say was that if you know the size of a code of minimal distance $k$ then this gives you a lower bound on $\chi$. Or you might look at the Lovasz $\theta$ of your graph (which can be computed by linear programming, in fact), and it will give you a lower bound on $\chi$. |