An Enumeration Problem for Sequences of n-ary Trees Arising from Algebraic Operads
Date
2019-02-04
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
Type
Thesis
Degree Level
Masters
Abstract
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.
Description
Keywords
combinatorics, operad theory, trees, plane trees, enumeration problems, discrete mathematics, forests, occupancy problem
Citation
Degree
Master of Science (M.Sc.)
Department
Mathematics and Statistics
Program
Mathematics