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URL:/combinatorics-and-optimization/events/graphs-and-m
 atroids-seminar-jane-gao-0
SUMMARY:Graphs and Matroids Seminar - Jane Gao
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Minors of random representable matroid over 
 finite fields\n\nSPEAKER:\n Jane Gao\n\nAFFILIATION:\n University of Water
 loo\n\nLOCATION:\n MC 5479\n\nABSTRACT: Consider a random n by m matrix A 
 over GF(q) where every\ncolumn has k nonzero elements\, and let M[A] be th
 e matroid represented\nby A. In the case that q=2\, Cooper\, Frieze and Pe
 gden (RSA 2019)\nproved that given a fixed binary matroid N\, if k is suff
 iciently\nlarge\, and m/n is sufficiently large (both depending on N)\, th
 en whp.\nM[A] contains N as a minor. We improve their result by determinin
 g the\nsharp threshold (of m/n) for the appearance of a fixed q-nary matro
 id\nN as a minor of M[A]\, for every k\\ge 3\, and every prime q. This is\
 njoint work with Peter Nelson.\n 
DTSTAMP:20250521T212501Z
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