Title: Bounds on the Number of Covers for Lattices and Related Posets

Dissertation Draft

Abstract: How many covers can there be in a lattice of order n? This question has gone unanswered for decades. In the pursuit of a couple of conjectures, one of which is nearly 40 years old, we have obtained novel results primarily related to asymptotic bounds for lattices and related posets. This talk will involve lattice theory, order theory, combinatorics, graph theory, and analysis.