MATH Seminar
| Title: Half Covering, Half Coloring |
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| Defense: Dissertation |
| Speaker: Alexander Clifton of Emory University |
| Contact: Alexander Clifton, alexander.james.clifton@emory.edu |
| Date: 2022-04-22 at 10:30AM |
| Venue: MSC W307C |
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| Abstract: We will discuss two types of problems in extremal combinatorics. First, we discuss problems about covering sets of points using affine hyperplanes. We consider a higher multiplicity generalization of a result of Alon and F\"{u}redi about the minimum number of hyperplanes needed to cover all but one vertex of an $n$-cube. We then discuss related covering problems for triangular grids. Next, we answer a question in arithmetic Ramsey theory. For a fixed set $D$, of positive integers, let $\Delta(D,k;2)$ be the smallest $N$ such that any $2$-coloring of $\{1,2,\cdots,N\}$ contains a monochromatic sequence $a_1 |
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