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Sizes of Invariant Sets of Random Permutations
Start Date: 11/17/2014Start Time: 3:00 PM
End Date: 11/17/2014End Time: 4:00 PM
Event Description
Robin Pemantle, Department of Mathematics, University of Pennsylvania

 

Abstract: Let M be a random set of integers greater than 1, containing each integer n independently with probability 1/n. Let S(M) be the sumset of M, that is, the set of all sums of subsets of M. How many independent copies of S must one intersect in order to obtain a finite set?

This problem is the limiting form of a problem arising in computational Galois theory. Dixon (1992) conjectured that O(1) was good enough, which was proved shortly thereafter by Luczak and Pyber. Their constant was 2^100 has not been improved until now, though is conjectured that it can be improved to 5 or 4. We show in fact that 4 sets suffice.

JOINT WORK WITH YUVAL PERES AND IGOR RIVIN
Contact Information:
Name: Ronald Perline
Email: rperline@math.drexel.edu
Location:
Korman Center, Room 245, 15 South 33rd Street, Philadelphia, PA 19104
Audience:
  • Public
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