Back to Search
Start Over
Counterexamples to a Conjecture of Dombi in Additive Number Theory
- Publication Year :
- 2022
- Publisher :
- arXiv, 2022.
-
Abstract
- We disprove a 2002 conjecture of Dombi from additive number theory. More precisely, we find examples of sets $A \subset \mathbb{N}$ with the property that $\mathbb{N} \setminus A$ is infinite, but the sequence $n \rightarrow |\{ (a,b,c) \, : \, n=a+b+c \text{ and } a,b,c \in A \}|$, counting the number of $3$-compositions using elements of $A$ only, is strictly increasing.<br />Comment: additional author added; largely rewritten with different example
- Subjects :
- FOS: Computer and information sciences
Mathematics - Number Theory
Discrete Mathematics (cs.DM)
Formal Languages and Automata Theory (cs.FL)
FOS: Mathematics
Mathematics - Combinatorics
Computer Science - Formal Languages and Automata Theory
Number Theory (math.NT)
Combinatorics (math.CO)
Computer Science - Discrete Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....0e1471343031a30d5893d128d86a77d0
- Full Text :
- https://doi.org/10.48550/arxiv.2212.12473