Integer solutions to interval linear equations and unique measurement
Peter C. Fishburn · Proceedings of the American Mathematical Society · 2000
Every system of n n linearly independent homogeneous linear equations in n + 1 n+1 unknowns with coefficients in { 1 , 0 , − 1 } \{1,0,-1\} has a unique (up to multiplication by − 1 -1 ) non-zero solution vector d = ( d 1 , d 2 , … , d n + 1 ) d= (d_1, d_2, \ldots , d_{n+1} ) in which the d j d_j ’s are integers with no common divisor greater than 1. It is known that, for large n n , | ∑ d j | | \sum d_j | can be arbitrarily greater than 2 n 2^n . We prove that if every equation, written as ∑ A x i − ∑ B x i = 0 \sum _A x_i - \sum _B x_i =0 , is such that