Nonnegative Radix Representations for the Orthant R
نویسندگان
چکیده
Let A be a nonnegative real matrix which is expanding i e with all eigenvalues j j and suppose that jdet A j is an integer Let D consist of exactly jdet A j nonnegativevectors inR We classify all pairs A D such that every x in the orthant Rn has at least one radix expansion in base A using digits inD The matrixAmust be a diagonalmatrix times a permutation matrix In addition A must be similar to an integer matrix but need not be an integer matrix In all cases the digit set D can be diagonally scaled to lie in Zn The proofs generalize a method of Odlyzko previously used to classify the one dimensional case
منابع مشابه
Nonnegative Radix Representations for the Orthant R N
Let A be a nonnegative real matrix which is expanding, i.e. all eigenvalues jj > 1. Suppose that j det(A)j is an integer and let D consists of exactly j det(A)j nonnegative vectors in R n. We classify all pairs (A; D) such that all x in the orthant R n + have at least one radix expansion using base A and digits in D. The matrix A must be a diagonal matrix times a permutation matrix. Also A must...
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تاریخ انتشار 1995