Orbits of rational n-sets of projective spaces under the action of the linear group

Details Orbits of rational n-sets of projective spaces under the action of the linear group Orbits of rational n-sets of projective spaces under the action of the linear group

2007-01-29

arxiv.org/abs/math/0701836v1

Mathematics

Combinatorics

Scientific paper

For a fixed dimension $N$ we compute the generating function of the numbers $t_N(n)$ (respectively $\bar{t}_N(n)$) of $PGL_{N+1}(k)$-orbits of rational $n$-sets (respectively rational $n$-multisets) of the projective space $\mathb{P}^N$ over a finite field $k=\mathbb{F}_q$. For $N=1,2$ these results provide concrete formulas for $t_N(n)$ and $\bar{t}_N(n)$ as a polynomial in $q$ with integer coefficients.

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