3.7.26. Autoref
A constraint that allows for modelling the autoref problem with a single constraint. The autoref problem is a generalisation of the problem of finding a magic serie and can be defined in the following way. Given an integer and an integer , the problem is to find a non-empty finite series such that (1)ย there are occurrences of in for each integer ranging from 0 to , and (2)ย . This leads to the following model:
23, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 5 and 23, 3, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 5 are the two unique solutions for and .