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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
comment 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
comment 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
comment 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
comment 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
comment 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
revised Mclaughlin Graph
edited tags
Jul
12
answered Mclaughlin Graph
Jul
11
comment 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
comment 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
comment 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
comment $\ell_o$ 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
comment 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
comment 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
comment 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 $\chi$.