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Linear hashing with partial expansions is a new file organization primarily intended for files which grow and shrink dynamically. This paper presents a mathematical analysis of the expected performance of the new scheme. The following measures are considered: length of successful and unsuccessful searches, accesses required to insert or delete a record, and the size of the overflow area. The performance is cyclical. For all performance measures, the necessary formulas are derived for computing the expected performance at any point of a cycle and the average over a cycle. Furthermore, the expected worst case in connection with searching is analyzed. The overall performance depends on several file parameters. The numerical results show that for many realistic parameter combinations the performance is expected to be extremely good. Even the longest search is expected to be of quite reasonable length.