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Monotonicity Although in practice most users will not have to face the issue, it is worth bearing in mind that recombination schemes 1 to 5 are not guaranteed to lead to monotonic resolution variables, i.e. it is NOT necessarily true that ${\rm min}\{d_{kB},d_{kl}\} \le {\rm min}\{d^{\prime}_{kB},d^{\prime}_{kl}\}$, where $d_k$ and $d_k^{\prime}$ are the resolution variables before and after recombination respectively. This means that, physically, the question ``How many jets are there at a particular scale $d$?'' may not have a unique answer. In KtJet, as should be clear from section 2.2, for a particular value of $d_\mathit{cut}$ set by findJetsD, the largest value of $N$ (i.e. the first place at which $d_\mathit{min} > d_\mathit{cut}$) will be returned by getNJets. Similarly, there may be no value of $d_\mathit{cut}$ for which a particular event has $N$ jets. There will however always be a $d_{min}$ value at which the event changed from $N+1$ to $N$ jets, which is the value returned by getDMerge. The above discussion also applies to the $y$ variables and associated methods.