Abstract
A 1-??? correspondence is established between partitions of a positive integer n of the form ( p 1 p 2 p 3… p n ) where p 1− p j+ k-1 ⩾2 and at most i−1 of the p j and partitions of n whose book differences d j all lie in the range −( i-2)⩽2 k- i-1. The same correspondence is also applied to partitions whose book differences lie in the range −( i-2)⩽ d jk ⩽2 k- i-2, and leads to further restrictions on the first set, and in particular to a correspondence between the partitions of a number n into distinct partsand the partitions of n whose book differences are all 0,1 or 2.
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