Seminar: Enumeration of Weakly Increasing 2-Noncrossing Trees
Speaker: Yvonne Kariuki, Kibabii University, Kenya
Abstract: This talk introduces and enumerates weakly increasing 2-noncrossing trees and their increasing variants. The study employs combinatorial analysis techniques to enumerate these tree structures according to multiple parameters including number of vertices, root degree, and number of forests. The methodology involves systematic application of generating function techniques implemented using SageMath for symbolic computation and verification of enumeration formulas. The analysis reveals that weakly increasing 2-noncrossing trees with n vertices are enumerated by a sequence which generalizes the little Schröder numbers when counting by root degree. The study also produces explicit formulas for counting these structures by number of forests. These results demonstrate significant connections between these tree structures and established combinatorial sequences. The findings extend the understanding of 2-noncrossing tree structures and their relationship to Schröder numbers, providing new enumeration results with applications in computational biology and analysis of RNA secondary structures.
Keywords: Combinatorics, 2-noncrossing trees, Schröder numbers, enumeration, bijections