Corpus ID: 236772748

An algorithm for counting arcs in higher-dimensional projective space

  title={An algorithm for counting arcs in higher-dimensional projective space},
  author={Kelly Isham},
  • K. Isham
  • Published 2 August 2021
  • Mathematics
An n arc in (k − 1)-dimensional projective space is a set of n points so that no k lie on a hyperplane. In 1988, Glynn gave a formula to count n-arcs in the projective plane in terms of simpler combinatorial objects called superfigurations. Several authors have used this formula to count n-arcs in the projective plane for n ≤ 10. In this paper, we determine a formula to count n-arcs in projective 3-space. We then use this formula to give exact expressions for the number of n-arcs in P3(Fq) for… 

Tables from this paper


A note on Nk configurations and theorems in projective space
  • D. Glynn
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2007
A method of embedding nk configurations into projective space of k–1 dimensions is given. It breaks into the easy problem of finding a rooted spanning tree of the associated Levi graph. Also it is
The Main Conjecture for MDS Codes
Theorems on the construction of an n-arc in P G, a set K of n points with at most k 1 in any hyperplane of the projective space of k 1 dimensions over Fq, and on the role of the set of n vectors in V, the vectorspace of k dimensions overFq, with any k linearly independent.
Arcs in finite projective spaces
This is an expository article detailing results concerning large arcs in finite projective spaces, which attempts to cover the most relevant results on arcs, simplifying and unifying proofs of known
Matroid Enumeration for Incidence Geometry
A new algorithm for the enumeration of non-isomorphic matroids is developed, using an encoding of oriented matroid axioms as a boolean satisfiability (SAT) problem, which succeeds to enumerate a complete list of the isomorph-free rank 4 matroIDS on 10 elements.
Open problems in finite projective spaces
Most of the objects studied in this paper have an interesting group; the classical groups and other finite simple groups appear in this way.
On planes through points off the twisted cubic in PG(3, q) and multiple covering codes
The structure of the point-plane incidence matrix in PG ( 3 , q ) with respect to the orbits of points and planes under the action of the stabilizer group of the twisted cubic is described to view generalized doubly-extended Reed-Solomon codes of codimension four as asymptotically optimal multiple covering codes.
Projective Geometries Over Finite Fields
1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. First properties of the plane 8. Ovals 9.
Linear spaces with at most 12 points
The 28,872,973 linear spaces on 12 points are constructed. The parameters of the geometries play an important role. In order to make generation easy, we construct possible parameter sets for
Graham Higman's PORC theorem
Graham Higman published two important papers in 1960‎. ‎In the first of these‎ ‎papers he proved that for any positive integer $n$ the number of groups of‎ ‎order $p^{n}$ is bounded by a polynomial
The theory of finite linear spaces - combinatorics of points and lines
This paper describes the implementation of n-Dimensional linear spaces in a discrete-time model and some examples show how the model can be modified for flows on rugous topographies varying around an inclined plane.