Extending t-designs |
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Authors: | WO Alltop |
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Institution: | Michelson Laboratories, Naval Weapons Center, China Lake, California 93555 USA |
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Abstract: | Three extension theorems for t-designs are proved; two for t even, and one for t odd. Another theorem guaranteeing that certain t-designs be (t + 1)-designs is presented. The extension theorem for odd t is used to show that every group of odd order 2k + 1, k ≠ 2r ? 1, acts as an automorphism group of a 2-(2k + 2, k + 1, λ) design consisting of exactly one half of the (k + 1)-settled, Although the question of the existence of a 6-(14, 7, 4) design is not settled, certain requisite properties of the 4-designs on 12 elements derived from such a design are established. All of these results depend heavily upon generalizations of block intersection number equations of N. S. Mendelsohn. |
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