# Counting arcs in projective planes via Glynn’s algorithm

@article{Kaplan2016CountingAI, title={Counting arcs in projective planes via Glynn’s algorithm}, author={Nathan Kaplan and Susie Kimport and Rachel Lawrence and Luke Peilen and Max Weinreich}, journal={Journal of Geometry}, year={2016}, volume={108}, pages={1013-1029} }

An n-arc in a projective plane is a collection of n distinct points in the plane, no three of which lie on a line. Formulas counting the number of n-arcs in any finite projective plane of order q are known for $$n \le 8$$n≤8. In 1995, Iampolskaia, Skorobogatov, and Sorokin counted 9-arcs in the projective plane over a finite field of order q and showed that this count is a quasipolynomial function of q. We present a formula for the number of 9-arcs in any projective plane of order q, even those…

## 5 Citations

### On the number of $k$-gons in finite projective planes

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- 2021

Let Π be a projective plane of order n and ΓΠ be its Levi graph (the point-line incidence graph). For fixed k ≥ 3, let c2k(ΓΠ) denote the number of 2k-cycles in ΓΠ. In this paper we show that c2k(ΓΠ)…

### Configurations of noncollinear points in the projective plane

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We consider the space $F_n$ of configurations of $n$ points in $P^2$ satisfying the condition that no three of the points lie on a line. For $n = 4, 5, 6$, we compute $H^*(F_n; \mathbb{Q})$ as an…

### Cohomology of moduli spaces of Del Pezzo surfaces.

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- 2019

We compute the rational Betti cohomology groups of the coarse moduli spaces of geometrically marked Del Pezzo surfaces of degree three and four as representations of the Weyl groups of the…

### On the cohomology of the space of seven points in general linear position

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- 2020

We determine the cohomology groups of the space of seven points in general linear position in the projective plane as representations of the symmetric group on seven elements by making equivariant…

### Seven points in general linear position

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- 2020

We determine the cohomology groups of the space of seven points in general linear position as representations of the symmetric group on seven elements by making equivariant point counts over finite…

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