Warianty tytułu
Języki publikacji
Abstrakty
Let p, q, rbe any three lines in the plane passing through a common point and suppose that O, P, Q, Rare any four collinear points such that P∈ p, Q ∈ q, R ∈ r, Pand Rare harmonic conjugates with respect to Oand Q(that is, │OP│/ │PQ│= │OR│/│QR│). For every k ≥2, we construct a set Xnof n= 4kpoints, which is distributed on the lines p, q, r, but each element of Xnᵕ{O} is incident to at most n/2 lines spanned by Xnᵕ{O}.(original abstract)
Słowa kluczowe
Twórcy
autor
- Uniwersytet Ekonomiczny we Wrocławiu
Bibliografia
- Akiyama J., Ito H., Kobayashi M., Nakamura G. (2011). Arrangements of n points whose incident-line-numbers are at most n/2. Graphs and Combinatorics. Vol. 27(3). Pp. 321-326.
- Beck J. (1983). On the lattice property of the plane and some problems of Dirac, Motzkin and Erdösin combinatorial geometry. Combinatorica. Vol. 3(3-4). Pp. 281-297.
- Brass P., Moser W.O.J., Pach J. (2005). Research Problems in Discrete Geometry. Springer Verlag.
- Coxeter H.S. (1961). Introduction to Geometry. John Wiley and Sons. New York
- Dirac G.A. (1951). Collinearity properties of sets of points. Quarterly J. Math. Vol. 2. Pp. 221-227.
- Grünbaum B. (1972). Arrangements and spreads. Regional Conference Series in Mathematics. Vol. 10. Amer. Math. Soc.
- Grünbaum B. (2010). Dirac's conjecture concerning high-incidence elements in aggregates. Geombinatorics. Vol. 20. Pp. 48-55.
- Motzkin T.S. (1951). The lines and planes connecting the points of a finite set. Trans. Amer. Math. Soc. Vol. 70. Pp. 451-464.
- Szemerédi E., Trotter W.T. (1983). Extremal problems in discrete geometry. Combinatorica. Vol. 3(3-4). Pp. 381-392.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171373085