Integer solutions to interval linear equations and unique measurement

Author:
Peter Fishburn

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1595-1599

MSC (2000):
Primary 05A99, 11D04, 91E45

DOI:
https://doi.org/10.1090/S0002-9939-00-05947-5

Published electronically:
November 15, 2000

MathSciNet review:
1814085

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Every system of linearly independent homogeneous linear equations in unknowns with coefficients in has a unique (up to multiplication by ) non-zero solution vector in which the 's are integers with no common divisor greater than 1. It is known that, for large , can be arbitrarily greater than . We prove that if every equation, written as , is such that and are intervals of contiguous indices, then . This confirms conjectures of the author and Fred Roberts that arose in the theory of unique finite measurement.

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Additional Information

**Peter Fishburn**

Affiliation:
AT&T Laboratories, Room C227, 180 Park Avenue, Florham Park, New Jersey 07932

Email:
fish@research.att.com

DOI:
https://doi.org/10.1090/S0002-9939-00-05947-5

Keywords:
Linear equations,
integer solutions,
measurement theory

Received by editor(s):
September 14, 1999

Published electronically:
November 15, 2000

Communicated by:
Mark J. Ablowitz

Article copyright:
© Copyright 2000
American Mathematical Society