The automorphism group of a flag-transitive 6–(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3–homogeneous permutation groups, the classification of flag-transi...The automorphism group of a flag-transitive 6–(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3–homogeneous permutation groups, the classification of flag-transitive 6-(v, k,2) designs can be discussed. In this paper, by analyzing the combination quantity relation of 6–(v, k, 2) design and the characteristics of 3-homogeneous permutation groups, it is proved that: there are no 6–(v, k, 2) designs D admitting a flag transitive group G ≤ Aut (D) of automorphisms.展开更多
In recent years, there has been a great deal of research concerning the flag- transitive t-designs, however, few about the block-transitive t-designs with t large （t 〉 4）. In 1993, Cameron and Praeger conjectured t...In recent years, there has been a great deal of research concerning the flag- transitive t-designs, however, few about the block-transitive t-designs with t large （t 〉 4）. In 1993, Cameron and Praeger conjectured that there are no non-trivial block-transitive 6-designs. In this paper, we prove that the conjecture is true when k ≤ 10000 and G ≤ Aut（D） is almost simple.展开更多
文摘The automorphism group of a flag-transitive 6–(v, k, 2) design is a 3-homogeneous permutation group. Therefore, using the classification theorem of 3–homogeneous permutation groups, the classification of flag-transitive 6-(v, k,2) designs can be discussed. In this paper, by analyzing the combination quantity relation of 6–(v, k, 2) design and the characteristics of 3-homogeneous permutation groups, it is proved that: there are no 6–(v, k, 2) designs D admitting a flag transitive group G ≤ Aut (D) of automorphisms.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10171006) the Youth Scientific Foundation of Beijing Normal University.
文摘In this paper, it is proved that the girth of a 4-homogeneous bipartite graph with valency greaterthan 2 is at most 12.
基金Supported by the National Natural Science Foundation of China （Grant No. 10871205, 11271208） and Hunan Provincial Science and Technology Department （2011FJ6092）.
文摘In recent years, there has been a great deal of research concerning the flag- transitive t-designs, however, few about the block-transitive t-designs with t large （t 〉 4）. In 1993, Cameron and Praeger conjectured that there are no non-trivial block-transitive 6-designs. In this paper, we prove that the conjecture is true when k ≤ 10000 and G ≤ Aut（D） is almost simple.
