Advertisement

Designs, Codes and Cryptography

, Volume 72, Issue 1, pp 1–5 | Cite as

Editorial: Special issue on finite geometries in honor of Frank De Clerck

  • John Bamberg
  • Jan De Beule
  • Nicola Durante
  • Michel Lavrauw
Article
  • 174 Downloads

This special issue of Designs, Codes, and Cryptography is dedicated to Prof. Frank De Clerck, full professor at the Mathematics Department of Ghent University since 1999, who has recently retired. The research articles appearing in this special issue are authored by selected mathematicians active in the field of Finite Geometry and Combinatorics. As a contribution to this special issue in honor of Prof. Frank De Clerck we find it most appropriate to include a short scientific biography.

Frank graduated from Ghent University where he remained for his PhD (completed in 1978) during which he studied partial geometries under the supervision of Joseph A. Thas. His thesis was titled “Een combinatorische studie van de eindige partiële meetkunden (en: A combinatorial study of finite partial geometries)”. During his career, his main research interests were situated in Finite Geometry and (Algebraic) Graph Theory, including \((\alpha ,\beta )\)

Keywords

Generalise Quadrangle Partial Geometry Exciting Location Quadratic Cone Finite Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Buekenhout, F., Lefèvre, C.: Generalized quadrangles in projective spaces. Arch. Math. (Basel) 25, 540–552 (1974)Google Scholar

Bibliography of Frank De Clerck

  1. 2.
    Thas, J.A., De Clerck, F.: Some applications of the fundamental characterization theorem of R. C. Bose to partial geometries. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 29(1–2), 86–90 (1976)Google Scholar
  2. 3.
    Thas, J.A., De Clerck, F.: Partial geometries satisfying the axiom of Pasch. Simon Stevin 51(3), 123–137 (1977/78)Google Scholar
  3. 4.
    De Clerck, F., Thas, J.A.: Partial geometries in finite projective spaces. Arch. Math. (Basel) 30(5), 537–540 (1978)Google Scholar
  4. 5.
    De Clerck, F.: Partial geometries–a combinatorial survey. Bull. Soc. Math. Belg. Sér. B 31(2), 135–145 (1979)Google Scholar
  5. 6.
    De Clerck, F.: The pseudogeometric and geometric \((t,\, s,\, s-1)\)-graphs. Simon Stevin 53(4), 301–317 (1979)Google Scholar
  6. 7.
    De Clerck, F., Thas, J.A.: Note on the extension of restricted \((r,\,\lambda )\)-designs. Ars. Comb. 7, 261–263 (1979)Google Scholar
  7. 8.
    De Clerck, F., Dye, R.H., Thas, J.A.: An infinite class of partial geometries associated with the hyperbolic quadric in PG\((4n--1,\,2)\). Eur. J. Comb. 1(4), 323–326 (1980)Google Scholar
  8. 9.
    Debroey, I., De Clerck, F.: Nontrivial \(\Gamma \Delta \)-regular graphs. Discret. Math. 41(1), 7–15 (1982)Google Scholar
  9. 10.
    De Clerck, F., Thas, J.A.: The embedding of \((0,\,\alpha )\)-geometries in PG\((n,\, q)\). I. In: Combinatorics ’81 (Rome, 1981), North-Holland Math. Stud., vol. 78, pp 229–240. North-Holland, Amsterdam (1983)Google Scholar
  10. 11.
    De Clerck, F.: Substructures of Partial Geometries. Quaderno 5 del Seminario di Geometrie Combinatorie, Università degli Studi de L’Aquila, pp. 1–16 (1984)Google Scholar
  11. 12.
    Thas, J.A., Debroey, I., De Clerck, F.: The embedding of \((0,\,\alpha )\)-geometries in PG\((n,\, q)\). II. Discret. Math. 51(3), 283–292 (1984)Google Scholar
  12. 13.
    De Clerck, F., Thas, J.A.: Exterior sets with respect to the hyperbolic quadric in PG\((2n-1, q)\). In: Finite geometries (Winnipeg, Man., 1984), Lecture Notes in Pure and Applied Mathematics, vol. 103, pp. 83–89. Dekker, New York (1985)Google Scholar
  13. 14.
    De Clerck, F.: Flocks di un cono in PG\((3, q)\). Quaderno 75 del Seminario di Geometrie Combinatorie “G. Tallini” (Roma), p. 8, (1987)Google Scholar
  14. 15.
    De Clerck, F., De Soete, M., Gevaert, H.: A characterization of the partial geometry \(T^*_2(K)\). Eur. J. Comb. 8(2), 121–127 (1987)Google Scholar
  15. 16.
    De Clerck, F., Gevaert, H., Thas, J.A.: Flocks of a quadratic cone in PG\((3, q),\;q\le 8\). Geom. Dedicata 26(2), 215–230 (1988)Google Scholar
  16. 17.
    De Clerck, F., Gevaert, H., Thas, J.A.: Translation partial geometries. In: Combinatorics ’86 (Trento, 1986), Annals of Discrete Mathematics, vol. 37, pp. 117–135. North-Holland, Amsterdam (1988)Google Scholar
  17. 18.
    De Clerck, F., Mazzocca, F.: The classification of polarities in reducible projective spaces. Eur. J. Comb. 9(3), 245–247 (1988)Google Scholar
  18. 19.
    De Clerck, F., Del Fra, A., Ghinelli, D.: Pointsets in partial geometries. In: Advances in finite geometries and designs (Chelwood Gate, 1990), Oxford Science Publishers, pp. 93–110. Oxford Univ. Press, New York (1991)Google Scholar
  19. 20.
    De Clerck, F., Gevaert, H., Thas, J.A.: Partial geometries and copolar spaces. In: Combinatorics ’88, (Ravello, 1988), Research Lecture Notes Mathematics, Vol. 1, pp. 267–280. Mediterranean, Rende (1991)Google Scholar
  20. 21.
    De Clerck, F., Johnson, N.L.: Subplane covered nets and semipartial geometries. Discret. Math., 106/107:127–134, 1992. A collection of contributions in honour of Jack van Lint.Google Scholar
  21. 22.
    De Clerck, F., Tonchev, V.D.: Partial geometries and quadrics. Sankhyā Ser. A, 54(Special Issue):137–145, 1992. Combinatorial mathematics and applications (Calcutta, 1988)Google Scholar
  22. 23.
    Thas, J.A., Herssens, C., De Clerck, F.: Flocks and partial flocks of the quadratic cone in PG\((3, q)\). In: Finite geometry and combinatorics (Deinze, 1992), London Math. Soc. Lecture Note Ser., vol. 191, pp. 379–393. Cambridge Univ. Press, Cambridge (1993)Google Scholar
  23. 24.
    De Clerck, F., Van Maldeghem, H.: On flocks of infinite quadratic cones. Bull. Belg. Math. Soc. Simon Stevin, 1(3):399–415, 1994. A tribute to J. A. Thas (Gent, 1994)Google Scholar
  24. 25.
    De Clerck, F., Van Maldeghem, H.: On linear representations of \((\alpha ,\beta )\)-geometries. Eur. J. Comb., 15(1):3–11, 1994. Algebraic combinatorics (Vladimir, 1991)Google Scholar
  25. 26.
    De Clerck, F., Van Maldeghem, H.: Some classes of rank \(2\) geometries. In: Handbook of incidence geometry, pp. 433–475. North-Holland, Amsterdam (1995)Google Scholar
  26. 27.
    De Clerck, F.: New partial geometries constructed from old ones. Bull. Belg. Math. Soc. Simon Stevin, 5(2–3):255–263, 1998. Finite geometry and combinatorics (Deinze, 1997)Google Scholar
  27. 28.
    De Bruyn, B., De Clerck, F.: Near polygons from partial linear spaces. Geom. Dedicata 75(3), 287–300 (1999)Google Scholar
  28. 29.
    De Bruyn, B., De Clerck, F.: On linear representations of near hexagons. Eur. J. Comb. 20(1), 45–60 (1999)Google Scholar
  29. 30.
    De Clerck, F., Delanote, M.: Partial geometries and the triality quadric. J. Geom. 68(1–2), 34–47 (2000)Google Scholar
  30. 31.
    De Clerck, F., Delanote, M.: Two-weight codes, partial geometries and Steiner systems. Des. Codes Cryptogr., 21(1–3):87–98, 2000. Special issue dedicated to Dr. Jaap Seidel on the occasion of his 80th birthday (Oisterwijk, 1999)Google Scholar
  31. 32.
    De Clerck, F., Hamilton, N., O’Keefe, C.M., Penttila, T.: Quasi-quadrics and related structures. Australas. J. Comb. 22, 151–166 (2000)Google Scholar
  32. 33.
    Cauchie, S., De Clerck, F., Hamilton, N.: Full embeddings of \((\alpha ,\beta )\)-geometries in projective spaces. Eur. J. Comb. 23(6), 635–646 (2002)Google Scholar
  33. 34.
    De Clerck, F., Delanote, M., Hamilton, N., Mathon, R.: Perp-systems and partial geometries. Adv. Geom. 2(1), 1–12 (2002)Google Scholar
  34. 35.
    Brown, M.R., De Clerck, F., Delanote, M.: Affine semipartial geometries and projections of quadrics. J. Combin. Theory Ser. A 103(2), 281–289 (2003)Google Scholar
  35. 36.
    De Clerck, F.: Partial and semipartial geometries: an update. Discret. Math., 267(1–3):75–86, (2003). Combinatorics 2000 (Gaeta)Google Scholar
  36. 37.
    De Clerck, F., Durante, N., Thas, J.A.: Dual partial quadrangles embedded in PG\((3, q)\). Adv. Geom., (suppl.):S224–S231 (2003). Special issue dedicated to Adriano BarlottiGoogle Scholar
  37. 38.
    De Clerck, F., De Winter, S., Thas, J.A.: A characterization of the semipartial geometries \(T_{2}^{\ast }(\cal U)\) and \(T_{2}^{\ast }(\cal B)\). Eur. J. Comb. 25(1), 73–85 (2004)Google Scholar
  38. 39.
    De Clerck, F., Delanote, M.: On \((0,\alpha )\)-geometries and dual semipartial geometries fully embedded in an affine space. Des. Codes Cryptogr. 32(1–3), 103–110 (2004)Google Scholar
  39. 40.
    De Clerck, F., De Feyter, N., Durante, N.: Two-intersection sets with respect to lines on the Klein quadric. Bull. Belg. Math. Soc. Simon Stevin 12(5), 743–750 (2005)Google Scholar
  40. 41.
    De Clerck, F., De Feyter, N., Thas, J.A.: Affine embeddings of \((0,\alpha )\)-geometries. Eur. J. Comb. 27(1), 74–78 (2006)Google Scholar
  41. 42.
    De Clerck, F., De Feyter, N.: Projections of quadrics in finite projective spaces of odd characteristic. Innov. Incid. Geom. 3, 51–80 (2006)Google Scholar
  42. 43.
    De Clerck, F., De Winter, S., Kuijken, E., Tonesi, C.: Distance-regular \((0,\alpha )\)-reguli. Des. Codes Cryptogr. 38(2), 179–194 (2006)Google Scholar
  43. 44.
    De Clerck, F., De Feyter, N.: A characterization of the sets of internal and external points of a conic. Eur. J. Comb. 28(7), 1910–1921 (2007)Google Scholar
  44. 45.
    De Clerck, F., De Feyter, N.: On connected line sets of antiflag class \([0,\alpha , q]\) in AG\((n, q)\). Eur. J. Comb. 29(6), 1427–1435 (2008)Google Scholar
  45. 46.
    Bamberg, J., De Clerck, F., Durante, N.: A hemisystem of a nonclassical generalised quadrangle. Des. Codes Cryptogr. 51(2), 157–165 (2009)Google Scholar
  46. 47.
    Bamberg, J., De Clerck, F.: A geometric construction of Mathon’s perp-system from four lines of PG\((5,3)\). J. Comb. Des. 18(6), 450–461 (2010)Google Scholar
  47. 48.
    Bamberg, J., De Clerck, F., Durante, N.: Intriguing sets in partial quadrangles. J. Comb. Des. 19(3), 217–245 (2011)Google Scholar
  48. 49.
    De Clerck, F., De Feyter, N.: A new characterization of projections of quadrics in finite projective spaces of even characteristic. Discret. Math. 311(13), 1179–1186 (2011)Google Scholar
  49. 50.
    De Clerck, F., De Winter, S., Maes, T.: A geometric approach to Mathon maximal arcs. J. Comb. Theory Ser. A 118(4), 1196–1211 (2011)Google Scholar
  50. 51.
    De Clerck, F., De Winter, S., Maes, T.: Partial flocks of the quadratic cone yielding Mathon maximal arcs. Discret. Math. 312(16), 2421–2428 (2012)Google Scholar
  51. 52.
    De Clerck, F., Durante, N.: Constructions and characterizations of classical sets in PG\((n, q)\). In: De Beule, J. and Storme, L. (eds.) Current research topics in Galois geometry, Mathematics Research Developments, chapter 1, pp. 1–33. Nova Science Publishers, New York (2012)Google Scholar
  52. 53.
    De Clerck, F., De Winter, S., Maes, T.: Singer 8-arcs of Mathon type in PG\((2,2^7)\). Des. Codes Cryptogr. 64(1–2), 17–31 (2012)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • John Bamberg
    • 1
  • Jan De Beule
    • 2
  • Nicola Durante
    • 3
  • Michel Lavrauw
    • 4
  1. 1.Centre for Mathematics of Symmetry and ComputationThe University of Western Australia (M019)CrawleyAustralia
  2. 2.Vakgroep zuivere wiskunde en computeralgebraUniversiteit GentGentBelgium
  3. 3.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Università degli Studi Napoli “Federico II”NapoliItaly
  4. 4.Dipartimento di Tecnica e Gestione dei Sistemi IndustrialiUniversità degli Studi di PadovaVicenzaItaly

Personalised recommendations