## Tilings and other combinatorial results

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In this dissertation we treat three tiling problems and three problems in combinatorial geometry, extremal graph theory and sparse Ramsey theory.

We first consider tilings of

In Chapter 3 we prove a conjecture of Lonc, stating that for any poset

The third tiling problem is about vertex-partitions of the hypercube graph

We follow up with a question in combinatorial geometry. A line in a planar set

We follow up with a problem in extremal graph theory. For any graph, we say that a given edge is triangular if it forms a triangle with two other edges. How few triangular edges can there be in a graph with

Finally, Chapter 7 is concerned with degrees of vertices in directed hypergraphs. One way to prescribe an orientation to an