Abstract
Some linear spaces are investigated and classified whose lines have precisely two distinct lengths which satisfy some arithmetical conditions.
Similar content being viewed by others
References
Batten L. M.: Linear spaces with line range n−1, n, n+1 and at most n2 points, J. Australian Math. Soc. (A) 29 (1980), 215–228.
Batten L. M., Totten J.: On a class of linear spaces with two consecutive line degrees, Ars Combinatoria 10 (1980), 107–114.
Batten L. M., de Witte P.: Finite linear spaces with two consecutive line degrees, Geom. Dedicata 14 (1983), 225–235.
Beth TH., Jungnickel D., Lenz H.: “Design Theory”, Bibliographisches Institut.Mannheim/Wien/Zurich, and Cambridge University Press, Cambridge 1985.
Buekenhout I., Delandtsheer Q., Doyen J.: Finite linear spaces with flag-transitive groups, Journal of Combinatorial Theory, Series A 49, (1988) 268–293.
Erdös P., Mullin R. C., Sos V. T., Stinson D. R.: Finite linear spaces and projective planes, Discrete Mathematics 47 (1983) 49–62 North-Holland.
Erdös P., Fowler J. C., Sos V. T., Wilson R. M.: On 2-De-signs, Journal of Combinatorial Theory, Series A 38 131–142 (1985).
Jungnickel D., Lenz H.: Minimal Linear Spaces, Journal of Combinatorial Theory, Series A 44, (1987), 229–240
Rees R.: Minimal clique partitions and pairwise balanced designs, Discr. Math. 61 (1986), 269–280.
Stinson D. R.: Applications and generalizations of the variance method in combinatorial designs, Utilitas Mathematica, Vol. 22 (1982), pp. 323–333.
Tallini G.: Spazi di rette finiti e k-insiemi di PG(r,q), Seminario di Geometrie Combinatorie diretto da Tallini G. n. 42 Agosto 1982, pp. 1–24.
Tallini G.: Spazi di rette finiti e k-insiemi di PG(r,q). Conferenze Semin. Mat. Univ. Bari 1984, pp. 1–24.
Wilson R.M.: An Existence Theory for Pairwise Balanced Designs, Journal of Combinatorial Theory (A) 13, (1972), 220–245.
Wilson R.M.: An Existence Theory for Pairwise Balanced Designs, III: Proof of the Existence Conjectures, Journal of Combinatorial Theory (A) 18, 1975, 71–79.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rajola, S. Some linear spaces with lines of two lengths. J Geom 36, 117–128 (1989). https://doi.org/10.1007/BF01231027
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01231027