The main results on the limiting distributions of incomplete U-statistics were developed in Blom (1976)¹ and Janson (1984)²; Lee (1990)³ gives a summary. However, for my taste, the proofs in Janson (1984) are somewhat hard to read. Lee (1990) improves upon those but has some inaccuracies---the main …

This post summarizes how one uses the repertoire method (as presented in Concrete Mathematics by Graham, Knuth and Patashnik). First we look at the repertoire method without the need for a radix-based solution and afterwards we discuss the solution given in the book for Exercise 16.

General method

Suppose we …