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Table 3 Number of combinations of pairs allocations of hamming distance from 0 to r

From: Multi-membership gene regulation in pathway based microarray analysis

Hamming Dist. Number of possible occurrences
0: 2n - 1
1: (2n- 1 - n)n + n(n -1) = (2n -2)n
2: 2 n - 1 - n 2 n 2 + n 2 n 2 - 1 = = n 2 2 n - 2
r: 2 n - 1 - n r n r + n r n r - 1 = = n r 2 n - 2
  1. Using the equations on Table 3 we can estimate the number of all possible combinations of allocations, represented as binary strings, of hamming distance from 1 to r