Expected Frobenius numbers
Iskander Aliev, Martin Henk, Aicke Hinrichs
TL;DR
This paper demonstrates that for large instances, the expected Frobenius number's order of magnitude aligns with its known lower bound, up to a constant depending on the dimension.
Contribution
It establishes the asymptotic behavior of the expected Frobenius number for large instances, connecting it to its lower bound.
Findings
Expected Frobenius number's magnitude matches its lower bound for large instances
The order of the expected Frobenius number is proportional to its lower bound
The constant of proportionality depends only on the dimension
Abstract
We show that for large instances the order of magnitude of the expected Frobenius number is (up to a constant depending only on the dimension) given by its lower bound.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Coding theory and cryptography · Graph theory and applications