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Published online by Cambridge University Press: 20 January 2009
An integer n may be partitioned into the set of integers (α1, α2, …, αl), where 
Whenever αi−1>αi the substitution of αi+1 for αi, where αi may be αi+1≡0, would give a partition of n+1 whilst the substitution of αi−1—1 for αi−1 would give a partition of n—1; partitions of n+1 and of n—1 so arising will be said to be associated with the given partition of n.
1 Rutherford, , Proc. Edinburgh Math. Soc., 7 (1942), 51–4.CrossRefGoogle Scholar
2 Rutherford, , loc. cit., &2.Google Scholar
3 Rutherford, , loc. cit., &3.Google Scholar
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