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SUMMARY:Nathanson Heights in Finite Vector Spaces - Joshua Batson (Cambrid
 ge/Yale)
DTSTART:20090204T141500Z
DTEND:20090204T151500Z
UID:TALK16173@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:Let p be a prime\, and let Zp denote the field of integers mod
 ulo p.  The Nathanson height of a point v in Zp^n is the sum of the least 
 nonnegative integer representatives of its coordinates.  The Nathanson hei
 ght of a subspace V of Zp^n is the least Nathanson height of any of its no
 nzero points.  In this talk\, I will investigate the range of the Nathanso
 n height function using a variety of techniques from additive combinatoric
 s.  In particular\, I will show that on subspaces of Zp^n of codimension o
 ne\, the Nathanson height function can only take values about p\, p/2\, p/
 3\, ..... affirmatively answering a question of Nathanson.  I prove this b
 y showing a similar result for the coheight on subsets of Zp\, where the c
 oheight of a subset A of Zp is the minimum number of times A must be added
  to itself so that the sum contains 0.  I will also present some open ques
 tions and conjectures related to the Nathanson height and coheight\, and i
 ndicate a few possible directions for future research.
LOCATION:MR12\, CMS
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