Geometry

Finite Geometry

51Exx

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  10. Laura Bader, Christine M. O'Keefe, and Tim Penttila, Some remarks on flocks, J. Aust. Math. Soc. 76 (2004), no. 3, 329–343.[MR]
  11. R. D. Baker, A. Bonisoli, A. Cossidente, and G. L. Ebert, Mixed partitions of PG(5,q), Discrete Math. 208/209 (1999), 23–29.[MR]
  12. R. D. Baker, J. M. N. Brown, G. L. Ebert, and J. C. Fisher, Projective bundles, Bull. Belg. Math. Soc. Simon Stevin 1 (1994), no. 3, 329–336.[MR]
  13. R. D. Baker, J. M. Dover, G. L. Ebert, and K. L. Wantz, Hyperbolic fibrations of PG(3,q), European J. Combin. 20 (1999), no. 1, 1–16.[MR]
  14. R. D. Baker, J. M. Dover, G. L. Ebert, and K. L. Wantz, Perfect Baer subplane partitions and three-dimensional flag-transitive planes, Des. Codes Cryptogr. 21 (2000), no. 1-3, 19–39.[MR]
  15. R. D. Baker and G. L. Ebert, A new class of translation planes, Combinatorics '86 (Trento, 1986), Ann. Discrete Math., vol. 37, North-Holland, Amsterdam, 1988, pp. 7–20.[MR]
  16. R. D. Baker and G. L. Ebert, Construction of two-dimensional flag-transitive planes, Geom. Dedicata 27 (1988), no. 1, 9–14.[MR]
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  18. R. D. Baker and G. L. Ebert, Intersection of unitals in the Desarguesian plane, in Proceedings of the Twentieth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1989), vol. 70, 1990, pp. 87–94.[MR]
  19. R. D. Baker and G. L. Ebert, On Buekenhout-Metz unitals of odd order, J. Combin. Theory Ser. A 60 (1992), no. 1, 67–84.[MR]
  20. R. D. Baker and G. L. Ebert, A Bruen chain for q = 19, Des. Codes Cryptogr. 4 (1994), no. 4, 307–312.[MR]
  21. R. D. Baker and G. L. Ebert, Filling the nest gaps, Finite Fields Appl. 2 (1996), no. 1, 42–61.[MR]
  22. R. D. Baker, G. L. Ebert, K. H. Leung, and Q. Xiang, A trace conjecture and flag-transitive affine planes, J. Combin. Theory Ser. A 95 (2001), no. 1, 158–168.[MR]
  23. R. D. Baker, G. L. Ebert, and K. L. Wantz, Regular hyperbolic fibrations, Adv. Geom. 1 (2001), no. 2, 119–144.[MR]
  24. R. D. Baker, G. L. Ebert, and K. L. Wantz, Enumeration of orthogonal Buekenhout unitals, Des. Codes Cryptogr. 55 (2010), no. 2-3, 261–283.[MR/doi]
  25. R. D. Baker and K. L. Wantz, Unitals in the code of the Hughes plane, J. Combin. Des. 12 (2004), no. 1, 35–38.[MR]
  26. Ronald D. Baker, C. Culbert, Gary L. Ebert, and Keith E. Mellinger, Odd order flag-transitive affine planes of dimension three over their kernel, Adv. Geom. 3 (2003), S215–S223.[MR]
  27. Ronald D. Baker, Jeremy M. Dover, Gary L. Ebert, and Kenneth L. Wantz, Baer subgeometry partitions, J. Geom. 67 (2000), no. 1-2, 23–34.[MR]
  28. Simeon Ball, Gary Ebert, and Michel Lavrauw, A geometric construction of finite semifields, J. Algebra 311 (2007), no. 1, 117–129.[MR]
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  31. Lynn M. Batten and Jeremy M. Dover, Blocking semiovals of type (1,M + 1,N + 1), SIAM J. Discrete Math. 14 (2001), no. 4, 446–457 (electronic).[MR]
  32. O. Bauduin, Géométries résiduellement faiblement primitives de pitits groupes affins, Master's Thesis, Université Libre de Bruxelles, 1999.
  33. Denis Bonheure, Francis Buekenhout, and Dimitri Leemans, On the Petrials of thin rank 3 geometries, J. Geom. 71 (2001), no. 1-2, 19–25.[MR]
  34. A. Bonisoli and A. Cossidente, Inscribed bundles, Veronese surfaces and caps, Geometry, Combinatorial Designs and Related Structures (Spetses, 1996), London Math. Soc. Lecture Note Ser., vol. 245, Cambridge Univ. Press, Cambridge, 1997, pp. 27–32.[MR]
  35. Arrigo Bonisoli and Antonio Cossidente, Mixed partitions of projective geometries, Des. Codes Cryptogr. 20 (2000), no. 2, 143–154.[MR]
  36. Arrigo Bonisoli and Gloria Rinaldi, A class of complete arcs in multiply derived planes, Adv. Geom. (2003), no. suppl., S113–S118.[MR]
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  38. F. Buekenhout and M. Hermand, On flag-transitive geometries and groups, Travaux de Mathématiques de l'Université Libre de Bruxelles 1 (1991), 45–78.
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  41. Francis Buekenhout, Philippe Cara, Michel Dehon, and Dimitri Leemans, Residually weakly primitive geometries of small sporadic and almost simple groups: a synthesis, Topics in Diagram Geometry, Quad. Mat., vol. 12, Dept. Math., Seconda Univ. Napoli, Caserta, 2003, pp. 1–27.[MR]
  42. Francis Buekenhout, Philippe Cara, and Koen Vanmeerbeek, Geometries of the group PSL(2,11), Geom. Dedicata 83 (2000), no. 1-3, 169–206.[MR]
  43. Francis Buekenhout, Michel Dehon, and Philippe Cara, Geometries of small almost simple groups based on maximal subgroups, Bull. Belg. Math. Soc. Simon Stevin (1998), no. suppl., ii+128.[MR]
  44. Francis Buekenhout, Michel Dehon, and Isabelle De Schutter, Projective injections of geometries and their affine extensions, J. Geom. 52 (1995), no. 1-2, 41–53.[MR]
  45. Francis Buekenhout, Michel Dehon, and Dimitri Leemans, All geometries of the Mathieu group M11 based on maximal subgroups, Experiment. Math. 5 (1996), no. 2, 101–110.[MR]
  46. Francis Buekenhout, Michel Dehon, and Dimitri Leemans, On flag-transitive incidence geometries of rank 6 for the Mathieu group M12, Groups and geometries (Siena, 1996), Trends Math., Birkhäuser, Basel, 1998, pp. 39–54.[MR]
  47. Francis Buekenhout, Michel Dehon, and Dimitri Leemans, An atlas of residually weakly primitive geometries for small groups, Acad. Roy. Belg. Cl. Sci. Mém. Collect. 8o (3) 14 (1999), 175.[MR]
  48. Francis Buekenhout and Dimitri Leemans, On a geometry of Ivanov and Shpectorov for the O'Nan sporadic simple group, J. Combin. Theory Ser. A 85 (1999), no. 2, 148–164.[MR]
  49. A. R. Calderbank, R. H. Hardin, E. M. Rains, P. W. Shor, and N. J. A. Sloane, A group-theoretic framework for the construction of packings in Grassmannian spaces, J. Algebraic Combin. 9 (1999), no. 2, 129–140.[MR]
  50. Philippe Cara, Exotische meetkunden van rang twee, PhD Thesis, Universite Libre De Bruxelles, 1994.
  51. Philippe Cara, An infinite family of Petersen geometries with nonlinear diagram, J. Geom. 67 (2000), no. 1-2, 73–88.[MR]
  52. Philippe Cara, RWPRI geometries for the alternating group A8, Finite Geometries, Dev. Math., vol. 3, Kluwer Acad. Publ., Dordrecht, 2001, pp. 61–97.[MR]
  53. Philippe Cara and Dimitri Leemans, The residually weakly primitive geometries of S5×2, Discrete Math. 255 (2002), no. 1-3, 35–45.[MR]
  54. Philippe Cara, Serge Lehman, and Dmitrii V. Pasechnik, On the number of inductively minimal geometries, Theoret. Comput. Sci. 263 (2001), no. 1-2, 31–35.[MR]
  55. A. Cossidente, Caps embedded in the Klein quadric, Bull. Belg. Math. Soc. Simon Stevin 7 (2000), no. 1, 13–19.[MR]
  56. A. Cossidente, C. Culbert, G. L. Ebert, and G. Marino, On m-ovoids of W3(q), Finite Fields Appl. 14 (2008), no. 1, 76–84.[MR]
  57. A. Cossidente, G. L. Ebert, and G. Korchmáros, Unitals in finite Desarguesian planes, J. Algebraic Combin. 14 (2001), no. 2, 119–125.[MR]
  58. A. Cossidente, G. L. Ebert, G. Marino, and A. Siciliano, Shult sets and translation ovoids of the Hermitian surface, Adv. Geom. 6 (2006), no. 4, 523–542.[MR]
  59. Antonio Cossidente, Gary L. Ebert, and Giuseppe Marino, A complete span of H(4,4) admitting PSL2(11) and related structures, Contrib. Discrete Math. 3 (2008), no. 1, 52–57.[MR]
  60. Antonio Cossidente and Tim Penttila, Hemisystems on the Hermitian surface, J. London Math. Soc. (2) 72 (2005), no. 3, 731–741.[MR]
  61. Antonio Cossidente and Tim Penttila, On m-regular systems on H(5,q2), J. Algebraic Combin. 29 (2009), no. 4, 437–445.[MR]
  62. Antonio Cossidente and Marialuisa J. de Resmini, The transitive and co-transitive blocking sets in P2(Fq), Contrib. Discrete Math. 3 (2008), no. 1, 47–51.[MR]
  63. Antonio Cossidente and Angelo Sonnino, Finite geometry and the Gale transform, Discrete Math. 310 (2010), no. 22, 3206–3210.[MR/doi]
  64. Antonio Cossidente and Sam K. J. Vereecke, Some geometry of the isomorphism Sp(4,q)≅O(5,q), q even, J. Geom. 70 (2001), no. 1-2, 28–37.[MR]
  65. Patricia Vanden Cruyce, Géométries des groupes PSL(2,q), PhD Thesis, Université Libre de Bruxelles, 1985.
  66. Alexander A. Davydov, Giorgio Faina, Stefano Marcugini, and Fernanda Pambianco, Computer search in projective planes for the sizes of complete arcs, J. Geom. 82 (2005), no. 1-2, 50–62.[MR]
  67. Michel Dehon, Classifying geometries with Cayley, J. Symbolic Comput. 17 (1994), no. 3, 259–276.[MR]
  68. Michel Dehon and Dimitri Leemans, Constructing coset geometries with Magma: An application to the sporadic groups M12 and J1, Atti Sem. Mat. Fis. Univ. Modena 50 (2002), no. 2, 415–427.[MR]
  69. Alice Devillers, Classification of Some Homogenous and Ultrahomogenous Structures, PhD Thesis, Université Libre de Bruxelles, 2002.
  70. Alice Devillers, A classification of finite partial linear spaces with a primitive rank 3 automorphism group of almost simple type, Innov. Incidence Geom. 2 (2005), 129–175.[MR]
  71. Cunsheng Ding, Zeying Wang, and Qing Xiang, Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in PG(3,32h+1), J. Combin. Theory Ser. A 114 (2007), no. 5, 867–887.[MR/arXiv]
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  76. G. L. Ebert, Spreads admitting regular elliptic covers, European J. Combin. 10 (1989), no. 4, 319–330.[MR]
  77. G. L. Ebert, Inverse planes with a given collection of common blocks, Discrete Math. 131 (1994), no. 1-3, 81–90.[MR]
  78. G. L. Ebert, Buekenhout-Tits unitals, J. Algebraic Combin. 6 (1997), no. 2, 133–140.[MR]
  79. G. L. Ebert, Replaceable nests, Mostly finite geometries (Iowa City, IA, 1996), Lecture Notes in Pure and Appl. Math., vol. 190, Dekker, New York, 1997, pp. 35–49.[MR]
  80. G. L. Ebert, Constructions in finite geometry using computer algebra systems, J. Symbolic Comput. 31 (2001), no. 1-2, 55–70.[MR]
  81. G. L. Ebert and J. W. P. Hirschfeld, Complete systems of lines on a Hermitian surface over a finite field, Des. Codes Cryptogr. 17 (1999), no. 1-3, 253–268.[MR]
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  83. M. Gailly, Géométries des groupes PSL(3,q), q < 7, Master's Thesis, Université Libre de Bruxelles, 2001.
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  85. Rohit Ghosh, Incompleteness of the Giulietti-Ughi arc for large primes, Discrete Math. 308 (2008), no. 17, 3824–3835.[MR]
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  91. Harald Gottschalk and Dimitri Leemans, The residually weakly primitive geometries of the Janko group J1, Groups and Geometries (Siena, 1996), Trends Math., Birkhäuser, Basel, 1998, pp. 65–79.[MR]
  92. Harald Gottschalk and Dimitri Leemans, Geometries for the group PSL(3,4), European J. Combin. 24 (2003), no. 3, 267–291.[MR]
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  96. M. Hermand, Géométries, language Cayley et groupe de Hall-Janko, PhD Thesis, Université Libre de Bruxelles, 1991.
  97. Pascale Jacobs and Dimitri Leemans, An algorithmic analysis of the intersection property, LMS J. Comput. Math. 7 (2004), 284–299 (electronic).[MR]
  98. Norman L. Johnson, Giuseppe Marino, Olga Polverino, and Rocco Trombetti, On a generalization of cyclic semifields, J. Algebraic Combin. 29 (2009), no. 1, 1–34.[MR/doi]
  99. Norman L. Johnson and Keith E. Mellinger, Multiple spread retraction, Adv. Geom. 3 (2003), no. 3, 263–286.[MR]
  100. Golala Abdulla Kadir, On the affine geometries of M24, PhD Thesis, University of Birmingham, 1984.
  101. J. D. Key, Codes and finite geometries, in Proceedings of the Twenty-ninth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1998), vol. 131, 1998, pp. 85–99.[MR]
  102. J. D. Key, Some applications of Magma in designs and codes: Oval designs, Hermitian unitals and generalized Reed-Muller codes, J. Symbolic Comput. 31 (2001), no. 1-2, 37–53.[MR]
  103. J. D. Key, T. P. McDonough, and V. C. Mavron, Partial permutation decoding for codes from affine geometry designs, J. Geom. 88 (2008), no. 1-2, 101–109.[MR]
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  109. Jennifer D. Key, Johannes Siemons, and Ascher Wagner, Regular sets on the projective line, J. Geom. 27 (1986), no. 2, 188–194.[MR]
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  113. Maska Law, Flocks, generalised quadrangles and translation planes from BLT-sets, PhD Thesis, University of Western Australia, 2003.
  114. Maska Law and Tim Penttila, Classification of flocks of the quadratic cone over fields of order at most 29, Adv. Geom. 3 (2003), no. Special Issue, S232–S244.[MR]
  115. Maska Law and Tim Penttila, Construction of BLT-sets over small fields, European J. Combin. 25 (2004), no. 1, 1–22.[MR]
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  117. Dimitri Leemans, Contribution á l'élaboration d'un Atlas de géométries: Volumes I and II, PhD Thesis, Universite Libre De Bruxelles, 1994.
  118. Dimitri Leemans, Classification of RWPRI Geometries for the Suzuki Simple Groups, PhD Thesis, Université Libre de Bruxeelles, 1998.
  119. Dimitri Leemans, The rank 2 geometries of the simple Suzuki groups Sz(q), Beiträge Algebra Geom. 39 (1998), no. 1, 97–120.[MR]
  120. Dimitri Leemans, Thin geometries for the Suzuki simple group Sz(8), Bull. Belg. Math. Soc. Simon Stevin 5 (1998), no. 2-3, 373–387.[MR]
  121. Dimitri Leemans, An atlas of regular thin geometries for small groups, Math. Comp. 68 (1999), no. 228, 1631–1647.[MR]
  122. Dimitri Leemans, The rank 3 geometries of the simple Suzuki groups Sz(q), Note Mat. 19 (1999), no. 1, 43–63 (2000).[MR]
  123. Dimitri Leemans, The residually weakly primitive geometries of the Suzuki simple group Sz(8), Groups St. Andrews 1997 in Bath, II, London Math. Soc. Lecture Note Ser., vol. 261, Cambridge Univ. Press, Cambridge, 1999, pp. 517–526.[MR]
  124. Dimitri Leemans, The residually weakly primitive geometries of the dihedral groups, Atti Sem. Mat. Fis. Univ. Modena 48 (2000), no. 1, 179–190.[MR]
  125. Dimitri Leemans, The residually weakly primitive pre-geometries of the Suzuki simple groups, Note Mat. 20 (2000/01), no. 1, 1–20.[MR]
  126. Dimitri Leemans, On a rank five geometry of Meixner for the Mathieu group M12, Geom. Dedicata 85 (2001), no. 1-3, 273–281.[MR]
  127. Dimitri Leemans, Some rank five geometries related to the Mathieu group M23, J. Combin. Theory Ser. A 95 (2001), no. 2, 365–372.[MR]
  128. Dimitri Leemans, The residually weakly primitive geometries of J2, Note Mat. 21 (2002), no. 1, 77–81.[MR]
  129. Dimitri Leemans, On a rank four geometry for the Hall-Janko sporadic group, J. Combin. Theory Ser. A 101 (2003), no. 1, 160–167.[MR]
  130. Dimitri Leemans, The residually weakly primitive geometries of M22, in Proceedings of the Conference on Finite Geometries (Oberwolfach, 2001), vol. 29, 2003, pp. 177–178.[MR]
  131. Dimitri Leemans, Constructions of rank five geometries for the Mathieu group M22, J. Geom. 79 (2004), no. 1-2, 146–155.[MR]
  132. Dimitri Leemans, The residually weakly primitive geometries of J3, Experiment. Math. 13 (2004), no. 4, 429–433.[MR]
  133. Dimitri Leemans, The residually weakly primitive geometries of M23, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 52 (2004), no. 2, 313–316 (2005).[MR]
  134. Dimitri Leemans, A generalization of a construction due to Van Nypelseer, Beiträge Algebra Geom. 46 (2005), no. 2, 561–574.[MR]
  135. Dimitri Leemans, The residually weakly primitive geometries of HS, Australas. J. Combin. 33 (2005), 231–236.[MR]
  136. Dimitri Leemans, Two rank six geometries for the Higman-Sims sporadic group, Discrete Math. 294 (2005), no. 1-2, 123–132.[MR]
  137. Christiane Lefèvre-Percsy, Nicolas Percsy, and Dimitri Leemans, New geometries for finite groups and polytopes, Bull. Belg. Math. Soc. Simon Stevin 7 (2000), no. 4, 583–610.[MR]
  138. Petr Lisoněk, Stefano Marcugini, and Fernanda Pambianco, Constructions of small complete arcs with prescribed symmetry, Contrib. Discrete Math. 3 (2008), no. 1, 14–19.[MR]
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  142. Stefano Marcugini, Alfredo Milani, and Fernanda Pambianco, Complete arcs in PG(2,25): the spectrum of the sizes and the classification of the smallest complete arcs, Discrete Math. 307 (2007), no. 6, 739–747.[MR]
  143. Justin McInroy and Sergey Shpectorov, On the simple connectedness of hyperplane complements in dual polar spaces. II, Discrete Math. 310 (2010), no. 8, 1381–1388.[MR/doi]
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  145. Keith E. Mellinger, Designs, Geometry, and a Golfer's Dilemma, Math. Mag. 77 (2004), no. 4, 275–282.[MR]
  146. Peter Müller and Gábor P. Nagy, A note on the group of projectivities of finite projective planes, Innov. Incidence Geom. 6/7 (2007/08), 291–294.[MR]
  147. F. Pambianco and L. Storme, Minimal blocking sets in PG(2,9), Ars Combin. 89 (2008), 223–234.[MR]
  148. Tim Penttila, Applications of computer algebra to finite geometry, Finite geometries, groups, and computation, Walter de Gruyter GmbH &Co. KG, Berlin, 2006, pp. 203–221.[MR]
  149. Tim Penttila and Blair Williams, Ovoids of parabolic spaces, Geom. Dedicata 82 (2000), no. 1-3, 1–19.[MR]
  150. Olga Polverino, Linear sets in finite projective spaces, Discrete Math. 310 (2010), no. 22, 3096–3107.
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