Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings
Abstract
Let a,b be positive integers. In this note, we study the numerical semigroup H=<a,a+1,b> and and the associated numerical semigroup ring R=k[[H]]. Under the certain conditions, we provide explicit formulas for the Frobenius number of H and for the first Hilbert coefficient of R.
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