scholarly journals Additive Number Theory and Inequalities in Ehrhart Theory

2015 ◽  
Vol 2016 (5) ◽  
pp. 1497-1540 ◽  
Author(s):  
Alan Stapledon
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Ehrhart Theory ◽  
Additive Number

Additive Number Theory

Science ◽  
1936 ◽  
Vol 84 (2176) ◽  
pp. 9-9
Author(s):  
Watson Davis
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Additive Number

scholarly journals Rectification Principles in Additive Number Theory

1998 ◽  
Vol 19 (3) ◽  
pp. 343-353 ◽  
Author(s):  
Y. F. Bilu ◽  
V. F. Lev ◽  
I. Z. Ruzsa
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Additive Number

A SURVEY OF FACTORIZATION COUNTING FUNCTIONS

2005 ◽  
Vol 01 (04) ◽  
pp. 563-581 ◽  
Author(s):  
A. KNOPFMACHER ◽  
M. E. MAYS
Keyword(s):  
Number Theory ◽  
Positive Integer ◽  
Additive Number Theory ◽  
Recursive Algorithms ◽  
Additive Number ◽  
Combinatorial Objects ◽  
Survey Techniques ◽  
Counting Functions ◽  
General Field ◽  
Positive Integers

The general field of additive number theory considers questions concerning representations of a given positive integer n as a sum of other integers. In particular, partitions treat the sums as unordered combinatorial objects, and compositions treat the sums as ordered. Sometimes the sums are restricted, so that, for example, the summands are distinct, or relatively prime, or all congruent to ±1 modulo 5. In this paper we review work on analogous problems concerning representations of n as a product of positive integers. We survey techniques for enumerating product representations both in the unrestricted case and in the case when the factors are required to be distinct, and both when the product representations are considered as ordered objects and when they are unordered. We offer some new identities and observations for these and related counting functions and derive some new recursive algorithms to generate lists of factorizations with restrictions of various types.

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