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Full-Text Articles in Discrete Mathematics and Combinatorics
Fuglede's Conjecture In Some Finite Abelian Groups, Thomas Fallon
Fuglede's Conjecture In Some Finite Abelian Groups, Thomas Fallon
Dissertations, Theses, and Capstone Projects
This dissertation thoroughly examines Fuglede's Conjecture within some discrete settings, shedding light on its intricate details. Fuglede's Conjecture establishes a profound connection between the geometric property of being a tiling set and the analytical attribute of being a spectral set. By exploring the conjecture on various discrete settings, this thesis delves into the implications and ramifications of the conjecture, unraveling its implications within the field.
Long Increasing Subsequences, Hannah Friedman
Long Increasing Subsequences, Hannah Friedman
HMC Senior Theses
In my thesis, I investigate long increasing subsequences of permutations from two angles. Motivated by studying interpretations of the longest increasing subsequence statistic across different representations of permutations, we investigate the relationship between reduced words for permutations and their RSK tableaux in Chapter 3. In Chapter 4, we use permutations with long increasing subsequences to construct a basis for the space of 𝑘-local functions.