Representations of integers by linear forms in nonnegative integers (1972)
by
Albert Nijenhuis
,
Herbert
,
S. Wilf
,
Communicated P. T. Bateman
| Venue: | J. Number Theory |
| Citations: | 15 - 1 self |
BibTeX
@ARTICLE{Nijenhuis72representationsof,
author = {Albert Nijenhuis and Herbert and S. Wilf and Communicated P. T. Bateman},
title = {Representations of integers by linear forms in nonnegative integers},
journal = {J. Number Theory},
year = {1972},
pages = {98--106}
}
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Abstract
Let Sz be the set of positive integers that are omitted values of the form f = z” = *1 a.x. $1) where the a, are fixed and relatively prime natural numbers and the xi are variable nonnegative integers. Set w = #Q and K = max 0 + 1 (the conductor). Properties of w and K are studied, such as an estimate for w (similar to one found by Brauer) and the inequality 2w> K. The so-called Gorenstein condition is shown to be equivalent to 2w = K. 1.
Citations
| 41 | On a problem on partitions - Brauer - 1942 |
| 32 | Mathematical questions with their solutions - Sylvester |
| 9 | The value-semigroup of a one-dimensional Gorenstein ring - Kunz - 1970 |
| 7 | An arithmetic theory of adjoint plane curves - Gorenstein - 1952 |
