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The Uniqueness of Odd Pair Designs
Author(s) -
Griggs J. R.
Publication year - 1978
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm19785811
Subject(s) - reversing , uniqueness , mathematics , combinatorics , order (exchange) , element (criminal law) , discrete mathematics , arithmetic , mathematical analysis , engineering , finance , automotive engineering , law , political science , economics
A pair design is an ordering of all pairs in {1, 2,…, n } such that pairs that share an element have at least [(n − 3)/2] pairs separating them. Such designs can be constructed for all n . We present a shorter proof of a result of Simmons and Davis, that pair designs for odd n are unique up to permuting the numbers or reversing the order of the pairs.