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http://hdl.handle.net/11375/28786
Title: | Comparing invariants of toric ideals of bipartite graphs |
Authors: | Bhaskara, Kieran |
Advisor: | Van Tuyl, Adam |
Department: | Mathematics and Statistics |
Keywords: | Mathematics;Commutative algebra;Combinatorics;Graph theory |
Publication Date: | 2023 |
Abstract: | Given a finite simple graph G, one can associate to G an ideal I_G, called the toric ideal of G. There are a number of algebraic invariants of ideals which are frequently studied in commutative algebra. In general, understanding these invariants is very difficult for arbitrary ideals. However, when the ideals are related to combinatorial objects, in this case, graphs, a deeper investigation can be conducted. If, in addition, the graph G is bipartite, even more can be said about these invariants. In this thesis, we explore a comparison of invariants of toric ideals of bipartite graphs. Our main result describes all possible values for the tuple (reg(K[E]/I_G), deg(h_{K[E]/I_G}), pdim(K[E]/I_G), depth(K[E]/I_G), dim(K[E]/I_G)) when G is a bipartite graph on n ≥ 1 vertices. |
URI: | http://hdl.handle.net/11375/28786 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Bhaskara_Kieran_2023july_msc.pdf | 564.05 kB | Adobe PDF | View/Open |
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