number of events (e.g. accidents, crimes, meetings, housing starts, hits on a web page)

An inversion of a sequence in computer science and discrete mathematics is a pair of terms in that sequence such that the components of those terms are out of their natural order.

$ \mathrm{inv}(A)=\#\{(A_{i},A_{j})\mid i<j{\,\,\mathrm{ and }\,\,}A_{i}>A_{j}\}

$ f(x + y) = f(x) + f(y) + \sum_i\sum_j c(x, i)c(y, j)[i > j]

code:python

init(N)

inv = 0

bit_add(a, 1)

inv += bit_sum(N) - bit_sum(a)

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