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Abstract This paper studies the p -Frobenius vector of affine semigroups S Nq S ⊂ N q. Defined with respect to a graded monomial order, the p -Frobenius vector represents the maximum element with at most p factorizations within S. We develop efficient algorithms for computing these vectors and analyze their behavior under the gluing operations with Nq N q.
Barroso et al. (Sat,) studied this question.