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The answer is yes, as the following paper makes clear: Beutelspacher, Albrecht. On parallelisms in finite projective spaces. Geometriae Dedicata 3 (1974), 35–40. According to the MSN review, …

I presume you're talking about characters over C. In which case Green's classic paper "The characters of the finite general linear groups" is the only thing I know on this subject. He defines a whole …

I came across this question when I was discussing the rather wonderful Devil's Chessboard Problem with my colleague, Francis Hunt. We realised that there is a nice connection to a packing question in …

If $f(x)$ is the associated polynomial to a circulant matrix $C$, then the kernel of $C$ is spanned by vectors $$v_i = (1,w_i,w_i^2, \dots, w_i^{n-1})$$ where the $w_i$ range through all $n$-th roots …

I suggest you refer to this paper: Cubic vertex-transitive graphs on up to 1280 vertices by Primoz Potocnik, Pablo Spiga and Gabriel Verret. The paper constructs the graphs in the title and, of …

Let me adjust notation slightly -- the $k$ in the original post is more usually a $\lambda$ in the literature. Thus the concept you want is this: Definition. A symmetric $2-(v,k,\lambda)$ design i …

The uniqueness of a Moore graph of degree 57 and diameter 2 is not known. See, for instance, this paper - http://www.sciencedirect.com/science/article/pii/S0024379509003735 - where they refer to `the …

Fix a positive integer $k>0$. For $p>k$ a prime, let $A_p$ be a subset of the finite field $\mathbb{Z}/p\mathbb{Z}$ of size $k$ which contains a primitive element. Define $G_p$ to be the (di)graph wh …

I'm interested in inequalities that guarantee the presence of cliques in incomplete block designs. Here's the set-up: I have an incidence structure $(V, B)$ which is an incomplete block design: $V$ is …

The behaviour of $F(n)$ varies dramatically with the prime-factorization of $n$. Typically one gets a large jump in the value of $F(n)$ as $n$ passes the power of a prime, particularly when that prime …

For the sake of getting this question off the unanswered stack, let me turn some of the comments into a question. Noam Elkies' comment: if one considers arbitrary subsets of $S_n$, then one can find …

This is really an comment to @Dima's answer, but it's a bit long... There is a classical result of Jordan in permutation group theory that says the following: If a primitive group $G$ [on a set o …

This question is probably going to turn into a community-wiki style list of favourite open problems concerning permutation groups and graphs. So, for what it's worth, here are two of mine: The Weiss …

$M_{13}$ is the Mathieu groupoid defined by Conway in Conway, J. H. $M_{13}$. Surveys in combinatorics, 1997 (London), 1–11, London Math. Soc. Lecture Note Ser., 241, Cambridge Univ. Press, Cam …

Let $\mathcal{C}$ be an abstract simplicial complex on some finite set $\Omega$. I say that a subset $\Lambda\subset\Omega$ is minimally non-simplicial if it is not a simplex, but all of its subsets a …