頁籤選單縮合
題 名 | From Planar Nearrings to Generating Blocks |
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作 者 | 孫新民; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 14:5 2010.10[民99.10] |
頁 次 | 頁1713-1739 |
分類號 | 314.91 |
關鍵詞 | Finite field; Balanced incomplete block design; Difference family; Planar nearring; |
語 文 | 英文(English) |
英文摘要 | Planar nearrings, like most of the subjects in finite geometries, can be applied for the construction of block designs. In this article we introduce the ideas of constructing simple BIBDs (balanced in complete block designs) from field-generated (or near field-generated) plan arnearrings. Further investigation reveals that there are strong connections between these kinds of constructions and the action of a sharply 2-transitive group on a set. We next explore the structures of the constructions. The theory is derived from finite fields directly. The main point is on finding a subset S (called generating block) of the field F with respect to the given stabilizer Stab F ∗ (S). A big portion of simple BIBDs with various parameters can be obtained in this way; many simple BIBDs with the same parameters appear. We classify the constructed BIBDs according to the types of the respective generating blocks. |
本系統中英文摘要資訊取自各篇刊載內容。