Browsing Mathematics (Faculty of) by Supervisor "Liu, Yu-Ru"
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Combinatorial Generalizations of Sieve Methods and Characterizing Hamiltonicity via Induced Subgraphs
(University of Waterloo, 2022-08-17)A sieve method is in effect an application of the inclusion-exclusion counting principle, and the estimation methods to avoid computing the explicit formula. Sieve methods have been used in number theory for over a hundred ... -
Problems in Combinatorial and Analytic Number Theory
(University of Waterloo, 2018-08-01)We focus on three problems in number theory. The first problem studies the random Fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single ... -
Some Problems in Multiplicative and Additive Number Theory
(University of Waterloo, 2020-07-27)In this thesis, we obtain several results in number theory. Let $k\geqslant 1$ be a natural number and $\omega_k(n)$ denote the number of distinct prime factors of a natural number $n$ with multiplicity $k$. We estimate ...