Frobenius numbers of generalized Fibonacci semigroups
نویسنده
چکیده
The numerical semigroup generated by relatively prime positive integers a1, . . . , an is the set S of all linear combinations of a1, . . . , an with nonnegative integral coefficients. The largest integer which is not an element of S is called the Frobenius number of S. Recently, J. M. Maŕın, J. L. Ramı́rez Alfonśın, and M. P. Revuelta determined the Frobenius number of a Fibonacci semigroup, that is, a numerical semigroup generated by a certain set of Fibonacci numbers. In this paper, we consider numerical semigroups generated by certain generalized Fibonacci numbers. Using a technique of S. M. Johnson, we find the Frobenius numbers of such semigroups obtaining the result of Maŕın et. al. as a special case. In addition, we determine the duals of such semigroups and relate them to the associated Lipman semigroups.
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