Cyclic digit run
= Cyclic digit run
A cyclic digit run is a consecutive segment of a digit string whose successive digits all increase by one or all decrease by one modulo the base. For example, $8,9,0,1$ is an increasing decimal run. This refers to cyclic digit values, not to joining the final position of the string back to its first position. Overlapping run constraints can be counted with the <inclusion-exclusion principle>.