Geometric proof of Rødseth's formula for Frobenius numbers

DOI10.1134/S0081543812010245zbMath1345.11022OpenAlexW2011246228MaRDI QIDQ741994

Alexey Ustinov

Publication date: 17 September 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543812010245

zbMATH Keywords

Frobenius numbersdouble-loop networkRødseth's formula

Mathematics Subject Classification ID

Continued fractions (11A55) Linear Diophantine equations (11D04) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (4)

Computational complexity of the original and extended diophantine Frobenius problem ⋮ The Frobenius number in the set of numerical semigroups with fixed multiplicity and genus ⋮ On the solutions of three-variable Frobenius-related problems using order reduction approach ⋮ Symmetric semigroups with three generators

Cites Work

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• Expected Frobenius numbers
• Limiting distribution of Frobenius numbers for \(n=3\)
• Frobenius problem for semigroups \(\mathbf S(d_1,d_2,d_3)\).
• The asymptotic distribution of Frobenius numbers
• On the geometry of the Frobenius problem
• Geometry of continued fractions associated with Frobenius numbers
• Analytic representations in the three-dimensional Frobenius problem
• Lattice translates of a polytope and the Frobenius problem
• On the linear diophantine problem of Frobenius
• Short generating functions for some semigroup algebras
• Weighted multi-connected loop networks
• Diameters of random circulant graphs
• On the distribution of Frobenius numbers with three arguments
• The mean value of Frobenius numbers with three arguments
• Integer Knapsacks: Average Behavior of the Frobenius Numbers
• A Linear Diophantine Problem
• A Minimal-Path Algorithm for the "Money Changing Problem"
• A Combinatorial Problem Related to Multimodule Memory Organizations
• On a linear Diophantine problem of Frobenius.
• The solution of Arnold's problem on the weak asymptotics of Frobenius numbers with three arguments
• Limit behaviour of large Frobenius numbers
• A complementary survey on double-loop networks

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