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Graduate Seminar
Math Club Seminar Joseph Briggs CMU Title: Extremal Collections of kUniform Vectors Abstract: How many vectors can you have with ten 1's, and the rest 0's, whose span have dimension at most some large r? As well as being a fun problem in its own right, this question arises naturally in the context of both coding theory and matroids. In this talk, we will see some instances where all weight10 vectors of length exactly r are the best we can do. Perhaps, that was the first example of such a collection of vectors you may think ofit appears to be remarkably robust across different (even infinite) fields, and even when swapping ``0'' with ``1''...but, once we go beyond $\mathbb{F}_2$, there are more letters to play with than just ``0'' and ``1'', so the number of variants on this question explodes! We can answer them all for $\mathbb{F}_3$, but not $\mathbb{F}_4$. Date: Tuesday, February 27, 2018 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Son Van 