Seminars & Colloquia Calendar
The constant in Shamir's Problem
Jeff Kahn - Rutgers University
Location: Hill 705
Date & time: Thursday, 08 March 2018 at 12:00PM - 1:00PM
Shamir's Problem (circa 1980) asks: for fixed r at least 3 and n a (large) multiple of r, how large should M be so that M random r-subsets of {1 ... n} are likely to contain a perfect matching (that is, n/r disjoint r-sets)? About ten years ago Johansson, Vu, and I proved the natural conjecture that this is true if M > C n ln n, for some large C=C(r). I can now show the asymptotically correct statement: the same behavior holds for any fixed C > 1/r.
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