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Minimal Presentations of Full Subsemigroups of ${\bf N}^2$
2001
Rocky Mountain Journal of Mathematics
We show that the cardinality of a minimal presentation for a two-dimensional full affine subsemigroup of N 2 minimally generated by p elements is , where G(S) denotes the subgroup of Z 2 spanned by S. In this paper we are going to assume that S is a full subsemigroup of N 2 such that rank (G(S)) = 2. (The case when rank (G(S)) ≤ 1 has no interest, because under this assumption with respect to the ordering a ≤ b if and only if b − a ∈ N 2 , then S is minimally generated by M . Furthermore, we
doi:10.1216/rmjm/1021249446
fatcat:pp4uovwhkbegvg6gnzrybbi2va