Provides a closed-form piecewise quadratic expression for the Frobenius number of shifted squares, obtained via combinatorial reduction, Lagrange's theorem, and generating functions.
Kannan, Lattice translates of a polytope and the Frobenius problem , Combinatorica
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A combinatorial reduction of the Frobenius problem to an optimization task produces explicit formulas for g(A), n(A), and s(A) on special sequences and applies MacMahon's partition analysis to count representations.
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On Frobenius Numbers of Shifted Power Sequences
Provides a closed-form piecewise quadratic expression for the Frobenius number of shifted squares, obtained via combinatorial reduction, Lagrange's theorem, and generating functions.
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A Combinatorial Approach to Frobenius Numbers of Some Special Sequences (Complete Version)
A combinatorial reduction of the Frobenius problem to an optimization task produces explicit formulas for g(A), n(A), and s(A) on special sequences and applies MacMahon's partition analysis to count representations.