Symmetric generalized numerical semigroups in Nd with embedding dimension 2 d + 1
Om Prakash Bhardwaj, Carmelo Cisto · Communications in Algebra · 2025
In this article, we classify all symmetric generalized numerical semigroups in Nd of embedding dimension 2d+1. Consequently, we show that in the case d>1, the property of being symmetric is equivalent to have a unique maximal gap with respect to natural partial order in Nd. Moreover, we deduce that when d>1, there does not exist any generalized numerical semigroup of embedding dimension 2d+1, which is almost symmetric but not symmetric.