Date on Master's Thesis/Doctoral Dissertation
8-2022
Document Type
Doctoral Dissertation
Degree Name
Ph. D.
Department
Mathematics
Degree Program
Applied and Industrial Mathematics, PhD
Committee Chair
Biro, Csaba
Committee Co-Chair (if applicable)
Kezdy, Andre
Committee Member
Kezdy, Andre
Committee Member
Riedel, Thomas
Committee Member
Seif, Steven
Committee Member
Bai, Lihui
Author's Keywords
Graph theory; partially ordered sets; Ramsey theory; interval orders; semi-orders; dimension theory
Abstract
In this dissertation, there are two major parts. One is the dimension results on different classes of partially ordered sets. We developed new tools and theorems to solve the bounds on interval orders using different number of lengths. We also discussed the dimension of interval orders that have a representation with interval lengths in a certain range. We further discussed the interval dimension and semi dimension for posets. In the second part, we discussed several related results on the Ramsey theory of grids, the results involve the application of Product Ramsey Theorem and Partition Ramsey Theorem
Recommended Citation
Wan, Sida, "Dimension and Ramsey results in partially ordered sets." (2022). Electronic Theses and Dissertations. Paper 3942.
https://doi.org/10.18297/etd/3942
