## Combinatorics '81: In Honour of Beniamino SegreCombinatorics '81 |

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### Contents

1 | |

5 | |

13 | |

17 | |

29 | |

37 | |

55 | |

61 | |

Chapter 40 Caps in elliptic quadrics | 449 |

Chapter 41 On Cohnfunctions | 467 |

Chapter 42 A class of strongIy regular graphs related to orthogonal groups | 469 |

Chapter 43 On the nonexistence of a semisymmetric 3design with 78 points | 473 |

Chapter 44 On certain linear congruence class geometries | 481 |

Chapter 45 Translation planes of characteristic p that admit SL2pr | 493 |

Chapter 46 Nondesarguesian planes partial geometries strongly regular graphs and codes arising from hyperbolic quadrics | 511 |

Chapter 47 The projectivity groups of ovals and of quadratic sets | 519 |

Chapter 9 Designs obtained from affine spaces | 77 |

Chapter 10 On the codes generated by certain divisible designs | 87 |

Chapter 11 On a characterization of the Grassmann spaces associated with an affne space | 95 |

Chapter 12 On a characterization of Grassmann space representing the hdimensional subspaces in a projective space | 113 |

Chapter 13 Enriched cliques with six vertices | 133 |

Chapter 14 Blocking sets in affine planes | 169 |

Chapter 15 Some building geometries of spherical type as sets of points and lines | 177 |

Chapter 16 Cyclic solutions for finite projective planes | 181 |

Chapter 17 Points and lines in metasymplectic spaces | 193 |

Chapter 18 On generalized perfect codes and Steiner systems | 197 |

Chapter 19 Greedy colouring of Steiner triple systems | 201 |

Chapter 20 Concurrence geometries | 209 |

Chapter 21 q2+q+1sets of type 012q+1 in translation planes of order q2 | 225 |

Chapter 22 The embedding of 0αgeometries in PGnq Part I | 229 |

Chapter 23 On cubic surfaces over a field of characteristic 3 | 241 |

Chapter 24 Some characterizations of finite 3 dimensional projective spaces and affineprojective planes | 279 |

Chapter 25 On a problem of A Kotzig | 283 |

Chapter 26 A small 4design | 291 |

Chapter 27 Some new generalizations of sharply t transitive groups and sets | 295 |

Chapter 28 Dissections of polygons | 315 |

Chapter 29 Group modifications of some partial groupoids | 319 |

Chapter 30 Bireflectionality | 333 |

Chapter 31 A graphic characterization of hermitian curves | 335 |

Chapter 32 On the connectivity of maximal planar graphs with minimum degree 5 | 343 |

Chapter 33 Affine geometries obtained from projective planes and skew resolutions on AG3q | 355 |

Chapter 34 Automorphisms and generalized incidence matrices of divisible designs | 377 |

Chapter 35 Some results on partial Steiner quadruple systems | 401 |

Chapter 36 Some recent results on cylic Steiner quadruple systems A survey | 409 |

Chapter 37 On a conjecture of S Ilkka | 419 |

Chapter 38 On homologies of fixedpointfree affine groups | 427 |

Chapter 39 On Pellegrinos 20 caps in S43 | 433 |

Chapter 48 On Rsequenceability and Rhsequenceability of groups | 535 |

Chapter 49 On the characterization of finite miquelin möbius planes | 549 |

Chapter 50 A physical characterization of conformal transformations of Minkowski spacetime | 567 |

Chapter 51 The van der waerden conjecture | 575 |

Chapter 52 Some extremal results about the genus of a pair of permutations | 581 |

Chapter 53 Partial parallelism spaces and slit spaces | 591 |

Chapter 54 On a class of kinematic spaces | 601 |

Chapter 55 A brief survey of covering radius | 617 |

Chapter 56 A graphic characterization of the lines of an affine space | 625 |

Chapter 57 Z2cohomology of projective spaces of odd order | 635 |

Chapter 58 Inequalities for point stable designs | 653 |

Chapter 59 On the structure of translation generalized quadrangles | 661 |

Chapter 60 Sur les karcs complets des planes de Galois dordre impair | 667 |

Chapter 61 The bundles axiom and egglike subsets of projective spaces | 695 |

Chapter 62 Kirkman cubes | 699 |

Chapter 63 Sulle ovali dei piani desarguesiani finiti dordine pari | 713 |

Chapter 64 Groups on points and sets | 721 |

Chapter 65 An application of combinatorics of Young tableaux to geomeric problems | 725 |

Chapter 66 Two characters ksets with respect to a singular space in PGrq | 731 |

Chapter 67 Moufang conditions of finite generalized quadrangles | 745 |

Chapter 68 Nilinearly generated nearalgebras | 753 |

Chapter 69 Affine planes and latin squares | 761 |

Chapter 70 Composition of rotations of graphs | 769 |

Chapter 71 A survey on varieties of PG4q and Baer subplanes of translation planes | 775 |

Chapter 72 On travalent graphs embedded in twisted honeycombs | 781 |

Chapter 73 Restricted Mispaces restricted Lispaces optimal codes and narcs | 789 |

Chapter 74 Sur des classes de groupes finis résolubles | 803 |

Chapter 75 Finite noneuclidean planes | 805 |

Chapter 76 Other talks | 819 |

List of participants | 821 |

### Common terms and phrases

affine geometry affine plane affine space algebraic assume automorphism group axiom belong Beniamino Segre called collinear collineation group combinatorial cone conic node consider construction contains copolar space covering radius cubic surfaces cyclic defined denote desarguesian dimension disjoint distinct points E-clique edges elements equation exactly exists finite fixed GF(p GF(q graph Grassmann space group G groupoid Hence hyperbolic hyperplane implies incidence structure integer intersect isomorphic k-set kinematic space latin squares Lemma Let G linear lines mapping Math matrix maximal subspace MCOLS meets F near-ring North-Holland Publishing Company nuclei obtained orbits order q orthogonal oval pair pairwise parallel class partial geometry partial groupoid permutation plane of order polar quadric prime projective plane projective space proof prop properties PROPOSITION prove punti punto quasigroup rank resp respectively result satisfies secant Segre skew spread-set Steiner subgroup subset tangent theorem translation planes tri-tangent triples unique vector vertices