Gaps in semigroups |
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Authors: | JL Ramírez Alfonsín |
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Institution: | Equipe Combinatoireet Optimisation - Case 189, Université Pierre et Marie Curie, Paris 6, 4 Place Jussieu, Paris 75252 Cedex 05, France |
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Abstract: | In this paper we investigate the behaviour of the gaps in numerical semigroups. We will give an explicit formula for the ith gap of a semigroup generated by k+1 consecutive integers (generalizing a result due to Brauer) as well as for a special numerical semigroup of three generators. It is also proved that the number of gaps of the numerical semigroup generated by integers p and q with g.c.d.(p,q)=1, in the interval pq-(k+1)(p+q),…,pq-k(p+q)] is equals to |
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Keywords: | 11B25 11B75 |
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