Frobenius problem for semigroups mathsf{S}(d_{1},d_{2},d_{3}) |
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Authors: | Leonid G. Fel |
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Affiliation: | (1) Department of Civil Engineering, Technion University, Haifa, 3200, Israel |
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Abstract: | We find the matrix representation of the set Δ(d 3), where d 3=(d 1,d 2,d 3), of integers that are unrepresentable by d 1,d 2,d 3 and develop a diagrammatic procedure for calculating the generating function Φ(d 3;z) for the set Δ(d 3). We find the Frobenius number F(d 3), the genus G(d 3), and the Hilbert series H(d 3;z) of a graded subring for nonsymmetric and symmetric semigroups and enhance the lower bounds of F(d 3) for symmetric and nonsymmetric semigroups. |
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Keywords: | Restricted partitions Frobenius problem Nonsymmetric and symmetric semigroups Hilbert series of a graded subring |
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