On p-Frobenius of Affine Semigroups

This paper studies the p-Frobenius vector of affine semigroups \(S\subset \mathbb {N}^q\) $S\subset {\mathbb{N}}^q$ . 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 \(\mathbb {N}^q\) ${\mathbb{N}}^q$ .