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Full-Text Articles in Set Theory
Abstractions Of The Game “Set”, Martin Grant
Abstractions Of The Game “Set”, Martin Grant
Master's Projects
Each card in the game of SET can be represented as a point in Z43, where Z3 is the f ield of 3 elements; an in-game position without any SETs can be represented as a cap set. We find the largest cap sets in Zn 3 for n ≤ 4 and prove their uniqueness. Then, we provide more insight into Ellenberg and Gijswijt’s proof of upper bound for the maximum size of cap set in Fnq, where Fq is the field of q elements, which they find to be o(cn …
The Sharpness Of Some Cluster Set Results, D. Rung, Samih Obaid
The Sharpness Of Some Cluster Set Results, D. Rung, Samih Obaid
Faculty Publications
We show that a recent cluster set theorem of Rung is sharp in a certain sense. This is accomplished through the construction of an interpolating sequence whose limit set is closed, totally disconnected and porous. The results also generalize some of Dolzenko's cluster set theorems.