Let S be a numerical monoid (i.e. an additive submonoid of n_0) with minimal generating set (n_1, ..., n_t). For m ∈S, if m = ∑_(i=1)~t x_i is called a factorization length of m. We denote by L(m) = {m_1, ..., m_k] (where m_i < m_(i+1) for each 1 ≤ i < k) the set of all possible factorization lengths of m.
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