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Combining Perfect Systems of Difference Sets
Author(s) -
Wild Peter
Publication year - 1986
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/18.2.127
Subject(s) - mathematics , perfect power , transitive relation , permutation (music) , prime (order theory) , combinatorics , permutation group , sequence (biology) , existential quantification , discrete mathematics , prime power , physics , biology , acoustics , genetics
We use sharply 2‐transitive permutation groups to construct an additive sequence of permutations from a system of difference sets, each component of which has size one less than a prime power. This allows us to combine perfect systems of difference sets to form other perfect systems. In particular, if there exists a perfect ( m, n + 1, 1)‐system and a perfect ( q, n + 1, 1)‐system then there exists a perfect ( mqn(n + 1) + m + q, n + 1, 1)‐system.
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