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Art of Computer Programming, Volume 4A, The: Combinatorial Algorithms, Part 1 by Donald E. Knuth

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7.2.1.3. Generating all combinations

Combinatorial mathematics is often described as “the study of permutations, combinations, etc.,” so we turn our attention now to combinations. A combination of n things, taken t at a time, often called simply a t-combination of n things, is a way to select a subset of size t from a given set of size n. We know from Eq. 1.2.6–(2) that there are exactly Image ways to do this; and we learned in Section 3.4.2 how to choose t-combinations at random.

Selecting t of n objects is equivalent to choosing the nt elements not selected. We will emphasize this symmetry by letting

throughout our discussion, and we will often ...

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