By M. Biliotti, A. Cossu, G. Korchmaros, A. Barlotti, G. Tallini

Curiosity in combinatorial suggestions has been enormously greater via the functions they could provide in reference to desktop know-how. The 38 papers during this quantity survey the state-of-the-art and document on contemporary leads to Combinatorial Geometries and their applications.

Contributors: V. Abatangelo, L. Beneteau, W. Benz, A. Beutelspacher, A. Bichara, M. Biliotti, P. Biondi, F. Bonetti, R. Capodaglio di Cocco, P.V. Ceccherini, L. Cerlienco, N. Civolani, M. de Soete, M. Deza, F. Eugeni, G. Faina, P. Filip, S. Fiorini, J.C. Fisher, M. Gionfriddo, W. Heise, A. Herzer, M. Hille, J.W.P. Hirschfield, T. Ihringer, G. Korchmaros, F. Kramer, H. Kramer, P. Lancellotti, B. Larato, D. Lenzi, A. Lizzio, G. Lo Faro, N.A. Malara, M.C. Marino, N. Melone, G. Menichetti, ok. Metsch, S. Milici, G. Nicoletti, C. Pellegrino, G. Pica, F. Piras, T. Pisanski, G.-C. Rota, A. Sappa, D. Senato, G. Tallini, J.A. Thas, N. Venanzangeli, A.M. Venezia, A.C.S. Ventre, H. Wefelscheid, B.J. Wilson, N. Zagaglia Salvi, H. Zeitler.

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S t a t . 23 ( 1 9 5 2 ) , 426-434. V. C e c c h e r i n i , Alcune o s s e r v a z i o n i s u l l a t e o r i a d e l l e r e t i . Rend. Acc. Naz. L i n c e i , 4 0 ( 1 9 6 6 ) , 218-221. R. H a l d e r , W. H e i s e , K o m b i n a t o r i k . H a n s e r V e r l a g , Munchen Wien 1976. - W. H e i s e , E s g i b t k e i n e n o p t i m a l e n (n+2,3)-Code e i n e r ungeraden Ordnung n . Math. Z . 164 ( 1 9 7 8 ) , 67-68. W. Heise, H. K a r z e l , L a g u e r r e und Minkowski-m-Strukturen.

Mn) such that the following two conditions are satisfied (the elements of B(t) are called blocks) (i) Through t distinct points which are parwise competitors there is exactly one block (ii) For every integer j with 1 5 j 5 n the following holds true: If D1 is the point intersection of j distinct columns (of MI, ),+I such that no two of them belong to the same M, and if D2 is another such intersection of j columns then # D1 = fc D2. , We denote a structure (MI, Mn; B(t)) by T(t,q,r,n). Conditions (i), (ii) serve as properties of balance.

N o w Lemma 3 and 4 show that every parallel of H is contained in exactly one of the sets Mi. 0 In the following corollary, we handle an important particular case. 2. Let S be a finite linear space of order n, and let H be a line with kH 5 n such that every point outside H has degree n+l. Let the integers d, x, z be defined in the following way: The number of lines of S is b = n2+n+l+z, kH = n+l-d, and H has exactly nd+x+z parallels in S . Suppose that there exists positive integers and 5 with the following properties: 1) n+l-d 5 kL 5 n+l-i for every parallel L of H.