By Jin Akiyama, Gisaku Nakamura (auth.), Jin Akiyama, Mikio Kano, Masatsugu Urabe (eds.)

This ebook constitutes the completely refereed post-proceedings of the japanese convention on Discrete Computational Geometry, JCDCG 2001, held in Tokyo, Japan in November 2001. The 35 revised papers provided have been conscientiously reviewed and chosen. one of the themes coated are polygons and polyhedrons, divissible dissections, convex polygon packings, symmetric subsets, convex decompositions, graph drawing, graph computations, element units, approximation, Delauny diagrams, triangulations, chromatic numbers, complexity, layer routing, effective algorithms, and illumination difficulties.

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Extra info for Discrete and Computational Geometry: Japanese Conference, JCDCG 2000 Tokyo, Japan, November 22–25, 2000 Revised Papers

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Ag = g-lag induces a f i x e d - p o i n t f r e e automorphism) o f K. Therefore a + aga-' is a b i j e c t i o n o f K onto K and so K i s inclosed i n the derived group F' o f F. The center Z(U) o f U i s n o t t r i v i a l and i f oU i s even, then U contains e x a c t l y one i n v o l u t i o n j: j a c t s on K sending k E K t o k - l (whence K i s commutative). Bartolone 40 group w i t h respect t o i t s s t a b i l i z e r , provided t h i s i s n o t t r i v i a l . More informa- t i o n about Frobenius groups and o t h e r e q u i v a l e n t d e f i n i t i o n s can be found i n [3].

9. - . BUlow-Str. 16 D 2300 K i e l F. R. Germany Annals of Discrete Mathematics 18 (1983) 37-54 0 North-Holland Publishing Company 37 ON SOME TRANSLATION PLANES ADMITTING A FROBENIUS GROUP OF COLLINEATIONS Claudio Bartolone I n t h i s n o t e we s t a t e some r e s u l t s concerning w i t h t r a n s l a t i o n planes o f dimension 2 over GF(q), where q = p Assume t h a t II r . From now on II w i l l denote such a plane. 2 has a c o l l i n e a t i o n group F o f order q (9-1) s a t i s f y i n g t h e f o l l o w i n g c o n d i t i o n : there e x i s t s a point V E Em such t h a t F f i x e s V und a c t s ( f a i t h f u l l y ) as a Frobenius group on i m - t V j .

K 21 42 bJ Cons ider a c o l l i n e a t i o n v o f N. J I f v i s i n h e r e n t t o t h e automorphismo o f = c (see l e n a 7), by s e t t i n g E ( C ) = o and ~ ( 0 =) 1 one d e f i n e s a ~ ) t h a t E ( X ) = 1 when x E o f G F ( Z ~i n t o A u ~ G F ( ~such D u { O } (lemma 8 ) . Let 0 be the equations which d e f i n e v according t o lemma 7. Then E ( C ) = o , -1 where we s e t c = c2c1 = ~ ( v ) . X. 5) gives c4 = ccac2. 8) we f i n d r e s p e c t i v e l y (a'(C)c)B = aBE(C)cc'l and ( a E ( c ) c ) y = = aY E ( C ) ~ 2 ~ 3Therefore .

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