Let S,T be two numerical semigroups. We study when S is one half of T, with T almost symmetric. If we assume that the type of T, t(T), is odd, then for any S there exist infinitely many such T and we prove that 1≤t(T)≤2t(S)+1. On the other hand, if t(T) is even, there exists such T if and only if S is almost symmetric and different from N; in this case the type of S is the number of even pseudo-Frobenius numbers of T. Moreover, we construct these families of semigroups using the numerical duplication with respect to a relative ideal.
One half of almost symmetric numerical semigroups
Strazzanti F.
2015-01-01
Abstract
Let S,T be two numerical semigroups. We study when S is one half of T, with T almost symmetric. If we assume that the type of T, t(T), is odd, then for any S there exist infinitely many such T and we prove that 1≤t(T)≤2t(S)+1. On the other hand, if t(T) is even, there exists such T if and only if S is almost symmetric and different from N; in this case the type of S is the number of even pseudo-Frobenius numbers of T. Moreover, we construct these families of semigroups using the numerical duplication with respect to a relative ideal.
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