Nonnegative Radix Representations for

the Orthant

Authors:
Jeffrey C. Lagarias and Yang Wang

Journal:
Trans. Amer. Math. Soc. **348** (1996), 99-117

MSC (1991):
Primary 11A63; Secondary 05B45, 39B42

DOI:
https://doi.org/10.1090/S0002-9947-96-01538-3

MathSciNet review:
1333392

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a nonnegative real matrix which is expanding, i.e. with all eigenvalues , and suppose that is an integer. Let consist of exactly nonnegative vectors in . We classify all pairs such that every in the orthant has at least one radix expansion in base using digits in . The matrix must be a diagonal matrix times a permutation matrix. In addition must be similar to an integer matrix, but need not be an integer matrix. In all cases the digit set can be diagonally scaled to lie in . The proofs generalize a method of Odlyzko, previously used to classify the one--dimensional case.

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Additional Information

**Jeffrey C. Lagarias**

Affiliation:
AT&T Bell Laboratories 600 Mountain Avenue Murray Hill, New Jersey 07974

Email:
jcl@research.att.com

**Yang Wang**

Affiliation:
School of Mathematics Georgia Institute of Technology Atlanta, Georgia 30332

Email:
wang@math.gatech.edu

DOI:
https://doi.org/10.1090/S0002-9947-96-01538-3

Received by editor(s):
July 1, 1994

Additional Notes:
Research supported in part by the National Science Foundation, grant DMS–9307601

Article copyright:
© Copyright 1996
American Mathematical Society