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Geometry Of Linear Subspace Arrangements With Connections To Matroid Theory, William Trok
Geometry Of Linear Subspace Arrangements With Connections To Matroid Theory, William Trok
Theses and Dissertations--Mathematics
This dissertation is devoted to the study of the geometric properties of subspace configurations, with an emphasis on configurations of points. One distinguishing feature is the widespread use of techniques from Matroid Theory and Combinatorial Optimization. In part we generalize a theorem of Edmond's about partitions of matroids in independent subsets. We then apply this to establish a conjectured bound on the Castelnuovo-Mumford regularity of a set of fat points.
We then study how the dimension of an ideal of point changes when intersected with a generic fat subspace. In particular we introduce the concept of a ``very unexpected hypersurface'' …
A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler
A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler
Senior Independent Study Theses
Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.