Representation functions of additive bases for abelian semigroups
A subset of an abelian semigroup is called an asymptotic basis for the semigroup if every element of the semigroup with at most finitely many exceptions can be represented as the sum of two distinct elements of the basis. The representation function of the basis counts the number of representations...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204306046 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | A subset of an abelian semigroup is called an asymptotic basis
for the semigroup if every element of the semigroup with at most
finitely many exceptions can be represented as the sum of two
distinct elements of the basis. The representation function of
the basis counts the number of representations of an element of
the semigroup as the sum of two distinct elements of the basis.
Suppose there is given function from the semigroup into the set
of nonnegative integers together with infinity such that this
function has only finitely many zeros. It is proved that for a large class of countably infinite
abelian semigroups, there exists a basis whose representation
function is exactly equal to the given function for every
element in the semigroup. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |