Joshua Cooper has authored 2 sequences.
A379299
a(n) is the maximum number k such that every permutation of the integers mod n admits at least k collinear triples.
Original entry on oeis.org
0, 0, 1, 0, 2, 0, 3, 0, 5, 2, 5, 0, 6, 9, 6, 4, 8
Offset: 1
a(5)=2 because the permutation (in one-line notation) 0,1,3,2,4 admits two collinear triples mod 5: {(0,0),(1,1),(4,4)} is on the line y=x and {(0,0),(3,2),(2,3)} is on the line y=4*x; and all other permutations admit at least 2 collinear triples.
- Joshua Cooper and Jack Hyatt, Permutations minimizing the number of collinear triples, arXiv:2501.02331 [math.CO], 2025. See p. 7.
- Joshua N. Cooper and József Solymosi, Collinear points in permutations, Ann. Comb. 9 (2005), no. 2, 169-175; preprint, arXiv:math/0408396 [math.CO], 2004.
- Liangpan Li, Collinear triples in permutations, Innov. Incidence Geom. 8 (2008), 171--173; arXiv preprint, arXiv:0805.0410 [math.CO], 2008.
A140468
Number of points at the n-th step of the following iteration, starting with four points in general position in the real projective plane: dualize the current pointset to a family of lines, take all intersections of those lines, repeat.
Original entry on oeis.org
4, 6, 7, 9, 13, 25, 97, 1741, 719725
Offset: 1
Joshua Cooper (cooper(AT)math.sc.edu), Jun 28 2008
a(2)=6 because four points in general position define six lines.
- K. Bezdek and J. Pach, A point set everywhere dense in the plane, Elem. Math. 40 (4) (1985) 81--84.
- Joshua Cooper, Mark Walters, Iterated point-line configurations grow doubly-exponentially, Discrete Comput. Geom. 43 (2010), no. 3, 554-562. MR2587837 (2011f:51016) 51M04 (52C35).
- Shalosh B. Ekhad, Doron Zeilberger, Enumerative Geometrical Genealogy (Or: The Sex Life of Points and Lines), arXiv:1406.5157 [math.CO], (19-June-2014)
- D. Ismailescu and R. Radoicic, A dense planar point set from iterated line intersections Comput. Geom. 27 (2004), no. 3, 257-267.
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