An Enumeration Problem for Sequences of n-ary Trees Arising from Algebraic Operads
Stasiuk, Daniel W 1992-
MetadataShow full item record
This thesis solves an enumeration problem for sequences of complete n-ary trees. Given the sequence of all complete n-ary plane trees with a given number of internal nodes (weight), in lexicographical order, we perform graftings with the basic n-ary tree to construct sets of sequences of trees of higher weight. Determining the number of elements of these sets solves a problem originating from the theory of free nonsymmetric operads, as the sets of sequences of trees are equivalent to spanning sets of homogeneous subspaces of a principal operad ideal. Two different solutions will be presented: one using recurrence relations and properties of forests, the other using occupancy problems.
DegreeMaster of Science (M.Sc.)
DepartmentMathematics and Statistics
CommitteeKhan, Shahedul; Bickis, Mik G; McQuillan, Ian; Soteros, Christine; Bremner, Murray R
Copyright DateJune 2019