TAILIEUCHUNG - Báo cáo toán học: "From a 1-rotational RBIBD to a Partitioned Difference Family."

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài:From a 1-rotational RBIBD to a Partitioned Difference Family. | From a 1-rotational RBIBD to a Partitioned Difference Family Marco Buratti Dipartimento di Matematica e Informatica Università di Perugia I-06123 Italy buratti@ Jie Yan and Chengmin Wang School of Science Jiangnan University Wuxi 214122 China wcm@j Submitted Nov 16 2008 Accepted Sep 15 2010 Published Oct 22 2010 Mathematics Subject Classification 05B05 05E18 Abstract Generalizing the case of A 1 given by Buratti and Zuanni Bull Belg. Math. Soc. 1998 we characterize the 1-rotational difference families generating a 1-rotational v k A -RBIBD that is a v k A resolvable balanced incomplete block design admitting an automorphism group G acting sharply transitively on all but one point TO and leaving invariant a resolution R of it. When G is transitive on R we prove that removing TO from a parallel class of R one gets a partitioned difference family a concept recently introduced by Ding and Yin IEEE Trans. Inform. Theory 2005 and used to construct optimal constant composition codes. In this way by exploiting old and new results about the existence of 1-rotational RBIBDs we are able to derive a great bulk of previously unnoticed partitioned difference families. Among our RBIBDs we construct in particular a 45 5 2 -RBIBD whose existence was previously in doubt. Keywords. 1-rotational RBIBD 1-rotational difference family partitioned difference family constant composition code. 1 Introduction Throughout the paper every union will be understood as multiset union. The union of ụ copies of a multiset A will be denoted by MA. Of course MA has a different meaning from M A as an example if A a b c then 2A a a b b c c while 2 A Research is supported by NSFCs under Grant No. 10801064 and 11001109 Tianyuan Mathematics Foundation of NSFC under Grant No. 10926103 Jiangnan University Foundation under Grant No. 2008LQN013 and Program for Innovative Research Team of Jiangnan University. THE ELECTRONIC JOURNAL OF COMBINATORICS 17 2010 R139 1 a b c a b c . .

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