Student Scholars Day

Non-Contiguous Pattern Containment in Trees

Henry Hall Atrium 39

We will define the containment of a full ordered binary tree within another binary tree in a non-contiguous sense. We then illustrate results regarding the number of non-contiguous containments of a particular $i$-leaf tree within all $j$-leaf trees. Also, we will apply generating functions into said results and into the enumeration of containing path trees within binary trees. We then present results, which can be generalized to $m$-ary trees. We first define what it means for a binary tree to contain another binary tree in a non-contiguous sense. We then enumerate non-contiguous containments of a $j$-leaf tree within all $i$-leaf trees. Our main result is that any two $j$-leaf trees are both contained within all $i$-leaf trees the same number of times, regardless of their shapes.