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By George E. Andrews, Peter Paule, Axel Riese (auth.), Anton Betten, Axel Kohnert, Reinhard Laue, Alfred Wassermann (eds.)

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Read or Download Algebraic Combinatorics and Applications: Proceedings of the Euroconference, Algebraic Combinatorics and Applications (ALCOMA), held in Gößweinstein, Germany, September 12–19, 1999 PDF

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Additional resources for Algebraic Combinatorics and Applications: Proceedings of the Euroconference, Algebraic Combinatorics and Applications (ALCOMA), held in Gößweinstein, Germany, September 12–19, 1999

Sample text

For instance (418 315 ) means that we look for a linear space which has 18 blocks of length 4 and 15 blocks of length 3. Similar as in [4] we compute for each line case the set of possible tactical decompositions which may arise as TDO of linear spaces ofthat type. We took only those line cases into the table where the parameter calculation produced at least one TDO-scheme. In the first three columns we give the number of the case, the line case and the number of TDO-schemes one gets in this case.

Remark: The choice of the permutation of the TDO-scheme and the choice of the intermediate tests may affect the computing time enormously. It seems a crucial problern to find good criteria for these choices. Otherwise one has to carry out long experiments to get a suitable conditioning for the computer run. Special attention was also needed for the following TDO-schemes: 9-1, 10-151, 10-293 and 16-97. Line cases 85 and 86 were done by transposing and using the order preserving program. There is a second TDO-scheme which produced many linear spaces, namely TDO-scheme 86-1 .

By the same method it is even possible to construct also the proper linear spaces on 18 points. In the present note we list the results in this case and point out some special spaces and situations. 2 Table of Results In this section, we present the classification of proper linear spaces on 18 points. We refer to [4] for all definitions and notions used in the following. Table 1 displays the numbers of proper linear spaces for the various line cases, i. e. distributions of block lengths. For instance (418 315 ) means that we look for a linear space which has 18 blocks of length 4 and 15 blocks of length 3.

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