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Full-Text Articles in Mathematics
Quantum Dimension Polynomials: A Networked-Numbers Game Approach, Nicholas Gaubatz
Quantum Dimension Polynomials: A Networked-Numbers Game Approach, Nicholas Gaubatz
Honors College Theses
The Networked-Numbers Game--a mathematical "game'' played on a simple graph--is incredibly accessible and yet surprisingly rich in content. The Game is known to contain deep connections to the finite-dimensional simple Lie algebras over the complex numbers. On the other hand, Quantum Dimension Polynomials (QDPs)--enumerative expressions traditionally understood through root systems--corresponding to the above Lie algebras are complicated to derive and often inaccessible to undergraduates. In this thesis, the Networked-Numbers Game is defined and some known properties are presented. Next, the significance of the QDPs as a method to count combinatorially interesting structures is relayed. Ultimately, a novel closed-form expression of …
On The Chromatic Numbers Of Subgroup Lattices, Jacob C. Miles
On The Chromatic Numbers Of Subgroup Lattices, Jacob C. Miles
MSU Graduate Theses
In this thesis we investigate the chromatic number of the Hasse diagram of a subgroup lattice. We combine results of Bollobás and Tůma to show that there exist infnite groups whose subgroup lattices have arbitarily high chromatic numbers. We show that fnite supersolvable groups have bipartite subgroup lattices but that CLT and non-solvable groups may not have bipartite subgroup lattices. Lastly, we give a preliminary argument suggesting that there are an infnite number of non-solvable groups whose subgroup lattices are bipartite.