Rises in forests of binary shrubs

In Bevan et al. (2016), the study of patterns in forests of binary shrubs was introduced. A k-ary heap H is a k-ary tree labeled with {1, . . . , n} such that every child has a larger label than its parent. Given a k-ary heap H , we associate a permutation σH with H by recording the vertex labels as they are encountered in the breadth-first search of the tree. For example, in Figure 1, we picture a 3-ary heap H whose associated permutation is σH = 1 6 2 3 7 10 8 9 5 4.