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micha
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Number of subgroups of finite abelian p-groups with a certain cotype.
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Number of subgroups of finite abelian p-groups with a certain cotype.
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What is the number of $2n\times 2n$-matrices $g=\begin{pmatrix} A & B \\\ C & -A^{t} \end{pmatrix}$, $B$ and $C$ symmetric, over the finite field $\mathbb{F}\_{q}$ with $\mathrm{rank}(g)=k$?
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What is the number of $2n\times 2n$-matrices $g=\begin{pmatrix} A & B \\\ C & -A^{t} \end{pmatrix}$, $B$ and $C$ symmetric, over the finite field $\mathbb{F}\_{q}$ with $\mathrm{rank}(g)=k$?
I need the above as a lemma to deduce some deaper results about distribution of special matrices over finite rings.
revised
What is the number of $2n\times 2n$-matrices $g=\begin{pmatrix} A & B \\\ C & -A^{t} \end{pmatrix}$, $B$ and $C$ symmetric, over the finite field $\mathbb{F}\_{q}$ with $\mathrm{rank}(g)=k$?
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What is the number of $2n\times 2n$-matrices $g=\begin{pmatrix} A & B \\\ C & -A^{t} \end{pmatrix}$, $B$ and $C$ symmetric, over the finite field $\mathbb{F}\_{q}$ with $\mathrm{rank}(g)=k$?
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What is the number of $2n\times 2n$-matrices $g=\begin{pmatrix} A & B \\\ C & -A^{t} \end{pmatrix}$, $B$ and $C$ symmetric, over the finite field $\mathbb{F}\_{q}$ with $\mathrm{rank}(g)=k$?