Skip to main content
SpringerLink
Log in
Book cover

Combinatorics pp 55–63Cite as

Combinatorics of Finite Geometries

  • Conference paper

  • 475 Accesses

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 16))

Abstract

In this lecture we intend to present a brief survey of very recent results. We shall be interested in the development of some topics considered in section 3.2 of Dembowski’s book [21] (Combinatorics of finite planes) and in problems connected with the existence of finite geometrical structures.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barlotti, A., Un ‘osservazione suite proprietà che caratterizzano un piano grafico finito, Boll. Un. Mat. Ital., 17 (1962) 394–398.

    MathSciNet  MATH  Google Scholar 

  2. Barlotti, A., Some classical and modem topics in finite geometrical structures, in: A survey of combinatorial theory, J.N. Srivastava a.o. (eds.), North-Holland Publ. Cy., Amsterdam, 1973.

    Google Scholar 

  3. Barlotti, A., Alcune questioni combinatorie netto studio dette strutture geometriche, in: Atti Convegno Teorie Combinatorie, Acc. Lincei, Rome 1973, to appear.

    Google Scholar 

  4. Basile, A., Sugli insiemi di proprietà che definiscono un piano grafico finito, Le Matematiche, 25 (1970) 84–95.

    MathSciNet  MATH  Google Scholar 

  5. Bernasconi, C., Strutture di incidenza connesse e definizione assiomatica di piani grafici e affini, Ann. Univ. Ferrara, to appear.

    Google Scholar 

  6. Bernasconi, C., Sistemi di assiomi che caratterizzano i disegni proiettivi, to appear.

    Google Scholar 

  7. Biscarini, P., Sets of axioms for finite inversive planes, to appear.

    Google Scholar 

  8. Bose, R.C., On a representation of Hughes planes, in: Proc. Internat. Conf. on Projective Planes, M.J. Kallaher & T.G. Ostrom (eds.), Washington State Univ. Press, 1973, pp.27–57.

    Google Scholar 

  9. Bramwell, D.L. & B.J. Wilson, The (11,3)-arcs of the Galois plane of order 5, Proc. Cambridge Philos. Soc., 74 (1973) 247–250.

    Article  MathSciNet  MATH  Google Scholar 

  10. Bruck, R.H., Construction problems in finite projective spaces, in: Finite geometric structures and their applications, c.i.m.e. II ciclo 1972, Ed. Cremonese, Rome, 1973, pp.105–188.

    Google Scholar 

  11. Bruen, A., Blocking sets in finite projective planes, Siam j. Appl. Math., 21 (1971) 380–392.

    Article  MathSciNet  MATH  Google Scholar 

  12. Bruen, A. & J.C. Fisher, Arcs and ovals in derivable planes, Math. z., 125 (1972) 122–128.

    Article  MathSciNet  MATH  Google Scholar 

  13. Bruen, A. & J.C. Fisher, Blocking-sets, k-arcs and nets of order ten, Advances in Math., 10 (1973) 317–320.

    Article  MathSciNet  MATH  Google Scholar 

  14. Bruijn, N.G. de & P. Erdös, On a combinatorial problem, Kon. Nederl. Akad. Wetensch. Proc. A, 51 (1948) 1277–1279

    MATH  Google Scholar 

  15. Bruijn, N.G. de & P. Erdös, On a combinatorial problem, (= Indag. Math., 10 (1948) 421–423)

    Google Scholar 

  16. Brutti, P., Sistemi di assiomi che definiscono un piano affine di ordine n, Ann. Univ. Ferrara Sez VII, 14 (1969) 109–118.

    MathSciNet  MATH  Google Scholar 

  17. Buekenhout, F. & R. Metz, On circular spaces having no disjoint circles, to appear.

    Google Scholar 

  18. Bumcrot, R. & D. Knee, private communication.

    Google Scholar 

  19. Cofman, J., On combinatorics of finite projective spaces, in: Proc. Internat. Conf. on Projective Planes, M.J. Kallaher & T.G. Ostrom (eds.), Washington State Univ. Press, 1973, pp.59–70.

    Google Scholar 

  20. Corsi, G., Sui sistemi minimi di assiomi atti a definite un piano grafico finito, Rendic. Sem. Mat. Padova, 34 (1964) 160–175.

    MathSciNet  MATH  Google Scholar 

  21. Crismale, M., Sui sistemi minimi di assiomi atti a definite un piano proiettivo finito, to appear.

    Google Scholar 

  22. Dembowski, P., Finite geometries, Ergebnisse der Mathematik 44, Springer-Verlag, Berlin etc., 1968.

    MATH  Google Scholar 

  23. Dembowski, P. & T.G. Ostrom, Planes of order n with oollineation groups of order n 2, Math. Z., 103 (1968) 239–258.

    Article  MathSciNet  MATH  Google Scholar 

  24. Dénes, J. & A.D. Keedwell, Latin squares and their applications, Acad. Press, New York and London, 1974.

    MATH  Google Scholar 

  25. Denniston, R.H.F., Some packings of projective spaces, Rend. Acc. Naz. Lincei (8), 52 (1972) 36–40.

    MathSciNet  MATH  Google Scholar 

  26. Denniston, R.H.F., Cyclic packings of the projective space of order 8, Rend. Acc. Naz. Lincei (8), 54 (1973) 373–377.

    MathSciNet  Google Scholar 

  27. Denniston, R.H.F., Packings of PG (3,q), in: Finite geometric structures and their applications, C.I.M.E. II ciclo 1972, Ed. Cremonese, Rome, 1973, pp.193–199.

    Google Scholar 

  28. Denniston, R.H.F., Spreads which are not subregular, Glasnik Mat. Ser. III, 8 (1973) 3–5.

    MathSciNet  Google Scholar 

  29. Denniston, R.H.F., Some spreads which contain reguli without being subregular, to appear.

    Google Scholar 

  30. Drake, D.A., Near affine Hjelmslev planes, J. Comb. Theory, 16 (1974) 34–50.

    Article  MathSciNet  MATH  Google Scholar 

  31. Hall, M. Jr., The theory of groups, Mac Millan, New York, 1959.

    MATH  Google Scholar 

  32. Hill, R., On the largest size of cap in S 5,3 , Rend. Acc. Naz. Lincei, to appear.

    Google Scholar 

  33. Hill, R., Caps and groups, to appear.

    Google Scholar 

  34. Hohler, P., Eigenschaften von vollständigen Systemen orthogonaler Lateinischer Quadrate, die bestimmte affine Ebenen repräsentieren, J. of Geometry 2 (1972) 161–174.

    Article  MathSciNet  MATH  Google Scholar 

  35. Magari, R., Sui sistemi di assiomi “minimali” per una data teoria, Boll. Un. Mat. Ital., 19 (1964) 423–435.

    MathSciNet  MATH  Google Scholar 

  36. Menichetti, G., q-archi completi nei piani di Hall di ordine q = 2 k, to appear.

    Google Scholar 

  37. Oliveri, U., Alcune proprietà che caratterizzano un piano affino finito, Le Matematiche, 22 (1967) 397–402.

    MathSciNet  MATH  Google Scholar 

  38. Ostrom, T.G., Semi translation planes, Trans. Amer. Math. Soc., 111 (1964) 1–18.

    Article  MathSciNet  MATH  Google Scholar 

  39. Pellegrino, G., Sul massimo ovdine delle calotte in S 4,q ’, Le Matematiche, 25 (1970) 149–157.

    MathSciNet  Google Scholar 

  40. Pellegrino, G., Procedimenti geometrici per la constvuzione di alcune classi di calotte complete in S r,3 , Boll. Un. Mat. Ital. (4), 5 (1972) 109–115.

    MathSciNet  MATH  Google Scholar 

  41. Reiman, I., Su una pvoprietà dei piani grafici finiti, Rend. Acc. Naz. Lincei, 35 (1963) 279–281.

    MathSciNet  MATH  Google Scholar 

  42. Reiman, I., Su una proprietà dei due disegni, Rend. Mat. e Appl., 1 (1968) 75–81.

    MathSciNet  MATH  Google Scholar 

  43. Segre, B., Proprietà elementari relative ai segmenti ed alle coniche sopra un campo qualsiasi ed una congettura di Seppa Ilkka per il caso dei campi di Galois, Ann. Mat. Pura Appl. (4), 96 (1973) 289–337.

    MathSciNet  MATH  Google Scholar 

  44. Tallini, G., Graphic characterization of algebraic varieties in a Galois space, in: Atti Convegno Teorie Combinatorie, Acc. Lincei, Rome 1973, to appear.

    Google Scholar 

  45. Tallini Scafati, M., The k-sets of type (m,n) in a Galois space S r,q (r≥2), in: Atti Convegno Teorie Combinatorie, Acc. Lincei, Rome 1973, to appear.

    Google Scholar 

  46. Thas, J.A., Connection between the n-dimensional affine space A n,q and the curve C, with equation y = x q , of the affine plane A 2,q n,Rend. Trieste, 2 (1970) 146–151.

    MathSciNet  MATH  Google Scholar 

  47. Thas, J.A., A combinatorial problem, Geometriae Dedicata, 1 (1973) 236–240.

    Article  MathSciNet  MATH  Google Scholar 

  48. Thas, J.A., 4-gonal configurations, in: Finite geometric structures and their applications, C.I.M.E. II ciclo 1972, Ed. Cremonese, Rome, 1973, pp.249–263.

    Google Scholar 

  49. Thas, J.A., On 4-gonal configurations, Geometriae Dedicata, 2 (1973) 317–326.

    Article  MathSciNet  MATH  Google Scholar 

  50. Thas, J.A., Flocks of finite egglike inversive planes, in: Finite geometric structures and their applications, C.I.M.E. II ciclo 1972, Ed. Cremonese, Rome, 1973, pp.189–191.

    Google Scholar 

  51. Thas, J.A., Some results concerning {(q+1)(n-1);n}-arcs and {(q+1)(n-1)+1;n}-arcs in finite projective planes of order q, to appear.

    Google Scholar 

  52. Thas, J.A., On 4-gonal configurations with parameters r = q 2 +1 and k = q+1, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universitá di Bologna, Bologna, Italy

    A. Barlotti

Authors
  1. A. Barlotti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. Hall Jr. J. H. van Lint

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Mathematical Centre, Amsterdam

About this paper

Cite this paper

Barlotti, A. (1975). Combinatorics of Finite Geometries. In: Hall, M., van Lint, J.H. (eds) Combinatorics. NATO Advanced Study Institutes Series, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1826-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-1826-5_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1828-9

  • Online ISBN: 978-94-010-1826-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation