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Experimental Mathematics
Article . 2016 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2014
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Automated Conjecturing of Frobenius Numbers via Grammatical Evolution

Authors: Nikola Adžaga;

Automated Conjecturing of Frobenius Numbers via Grammatical Evolution

Abstract

Conjecturing formulas and other symbolic relations occurs frequently in number theory and combinatorics. If we could automate conjecturing, we could benefit not only from speeding up, but also from finding conjectures previously out of our grasp. Grammatical evolution, a genetic programming technique, can be used for automated conjecturing in mathematics. Concretely, this work describes how one can interpret the Frobenius problem as a symbolic regression problem, and then apply grammatical evolution to it. In this manner, a few formulas for Frobenius numbers of specific quadruples were found automatically. The sketch of the proof for one conjectured formula, using lattice point enumeration method, is provided as well. Same method can easily be used on other problems to speed up and enhance the research process.

8 pages, 2 tables; added a clear introduction, otherwise reduced text significantly

Related Organizations
Keywords

grammatical evolution, Mathematics - Number Theory, FOS: Mathematics, Mathematics - Combinatorics, Frobenius number, Number Theory (math.NT), Combinatorics (math.CO), automated conjecturing ; Frobenius number ; grammatical evolution, automated conjecturing

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green
bronze