Frobenius Problem for Semigroups S (d1, d2, d3)
نویسنده
چکیده
The matrix representation of the set ∆(d), d = (d1, d2, d3), of the integers which are unrepresentable by d1, d2, d3 is found. The diagrammatic procedure of calculation of the generating function Φ ( d; z ) for the set ∆(d) is developed. The Frobenius number F ( d ) , genus G ( d ) and Hilbert series H(d; z) of a graded subring for non–symmetric and symmetric semigroups S ( d ) are found. The upper bound for the number of non–zero coefficients in the polynomial numerators of Hilbert series H(dm; z) of graded subrings for non–symmetric semigroups S (dm) of dimension, m ≥ 4, is established.
منابع مشابه
Analytic Representations in the 3-dim Frobenius Problem
We consider the Diophantine problem of Frobenius for semigroup S ( d ) where d denotes the tuple (d1, d2, d3), gcd(d1, d2, d3) = 1. Based on the Hadamard product of analytic functions [17] we have found the analytic representation for the diagonal elements akk ( d ) of the Johnson’s matrix of minimal relations [12] in terms of d1, d2, d3. Bearing in mind the results of the recent paper [10] thi...
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