Preface |
Introduction / 1: |
Definition of near polygon / 1.1: |
Genesis / 1.2: |
Near polygons with an order / 1.3: |
Parallel lines / 1.4: |
Substructures / 1.5: |
Product near polygons / 1.6: |
Existence of quads / 1.7: |
The point-quad and line-quad relations / 1.8: |
Some classes of near polygons / 1.9: |
Generalized quadrangles of order (2, t) / 1.10: |
Dense near polygons / 2: |
Main results / 2.1: |
The existence of convex subpolygons / 2.2: |
Proof of Theorem 2.6 / 2.3: |
Upper bound for the diameter of Γd(x) / 2.4: |
Upper bounds for t + 1 in the case of slim dense near polygons / 2.5: |
Slim dense near polygons with a big convex subpolygon / 2.6: |
Regular near polygons / 3: |
Some restrictions on the parameters / 3.1: |
Eigenvalues of the collinearity matrix / 3.3: |
Upper bounds for t / 3.4: |
Slim dense regular near hexagons / 3.5: |
Slim dense regular near octagons / 3.6: |
Glued near polygons / 4: |
Characterizations of product near polygons / 4.1: |
Admissible δ-spreads / 4.2: |
Construction and elementary properties of glued near polygons / 4.3: |
Basic characterization result for glued near polygons / 4.4: |
Other characterizations of glued near polygons / 4.5: |
Subpolygons / 4.6: |
Glued near polygons of type δ ∈ {0, 1} / 4.7: |
Valuations / 5: |
Nice near polygons / 5.1: |
Valuations of nice near polygons / 5.2: |
Characterizations of classical and ovoidal valuations / 5.3: |
The partial linear space Gf / 5.4: |
A property of valuations / 5.5: |
Some classes of valuations / 5.6: |
Valuations of dense near hexagons / 5.7: |
Proof of Theorem 5.29 / 5.8: |
Proof of Theorem 5.30 / 5.9: |
Proof of Theorem 5.31 / 5.10: |
Proof of Theorem 5.32 / 5.11: |
The known slim dense near polygons / 6: |
The classical near polygons DQ(2n, 2) and DH(2n − 1,4) / 6.1: |
The class Hn / 6.2: |
The class Gn / 6.3: |
The class In / 6.4: |
The near hexagon E1 / 6.5: |
The near hexagon E2 / 6.6: |
The near hexagon E3 / 6.7: |
The elements of C3 and C4 / 6.8: |
Slim dense near hexagons / 7: |
Elementary properties of slim dense near hexagons / 7.1: |
Case I: <$>{\cal S}<$> is a regular near hexagon / 7.3: |
Case II: <$>{\cal S}<$> contains grid- and W(2)-quads but no Q(5, 2)-quads / 7.4: |
Case III: <$>{\cal S}<$> contains grid- and Q(5, 2)-quads but no W(2)-quads / 7.5: |
Case IV: <$>{\cal S}<$> contains W(2)- and Q(5, 2)-quads but no grid-quads / 7.6: |
Case V: <$>{\cal S}<$> contains grid-quads, W(2)-quads and Q(5,2)-quads / 7.7: |
Appendix / 7.8: |
Slim dense near polygons with a nice chain of subpolygons / 8: |
Overview / 8.1: |
Proof of Theorem 8.1 / 8.2: |
Proof of Theorem 8.2 / 8.3: |
Proof of Theorem 8.3 / 8.4: |
Proof of Theorem 8.4 / 8.5: |
Proof of Theorem 8.5 / 8.6: |
Proof of Theorem 8.6 / 8.7: |
Proof of Theorem 8.7 / 8.8: |
Proof of Theorem 8.8 / 8.9: |
Proof of Theorem 8.9 / 8.10: |
Slim dense near octagons / 9: |
Some properties of slim dense near octagons / 9.1: |
Existence of big hexes / 9.2: |
Classification of the near octagons / 9.3: |
Nondense slim near hexagons / 10: |
A few lemmas / 10.1: |
Slim near hexagons with special points / 10.2: |
Slim near hexagons without special points / 10.3: |
Proof of Theorem 10.8 / 10.4: |
Proof of Theorem 10.9 / 10.5: |
Proof of Theorem 10.10 / 10.6: |
Slim near hexagons with an order / 10.7: |
Dense near polygons of order (3, t) / A: |
Generalized quadrangles of order (3, t) / A.1: |
Dense near hexagons of order (3, t) / A.2: |
Dense near octagons of order (3, t) / A.3: |
Some properties of dense near 2d-gons of order (3, t) / A.4: |
Dense near polygons of order (3, t) with a nice chain of subpolygons / A.5: |
Bibliography |
Index |
Preface |
Introduction / 1: |
Definition of near polygon / 1.1: |