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Summary form only given; substantially as follows. Computing with sets of tuples (n-ary relations) is often required in programming, while being a major cause of performance degradation as the size of sets increases. The authors present a new data structure dedicated to the manipulation of large sets of tuples, dubbed a sharing tree. The main idea to reduce memory consumption is to share some sub-tuples of the set represented by a sharing tree. Various conditions are given. The authors have developed algorithms for common set operations: membership, insertion, equality, union, intersection, ... that have theoretical complexities proportional to the sizes of the sharing trees given as arguments, which are usually much smaller than the sizes of the represented sets.