BALANCED ZERO-SUM SEQUENCES AND MINIMAL INTRINSIC EXTENSIONS (Model theoretic aspects of the notion of independence and dimension)

Abstract

Let a and b be positive real numbers. Assume that a/b is a rational number. Let v be a finite zero-sum sequence with entries from {a, -b}. We say that v has the positively balanced prefix property if 0<displaystyle sum u<a+b for any proper prefix u of v. We say that v is balanced if |displaystyle sum u|<a+b for any consecutive subsequence u of v. There exists uniquely a sequence s having the positively balanced prefix property. Any rotations of s^{k} are balanced. Conversely, any balanced sequence is a rotation of s^{k}.