2025/01/21 by Hyunsoo Cho, Kyeongjun Lee, Hayan Nam · 1 citation
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Algebraic Geometry and Number Theory
paper · doi:10.1080/00927872.2024.2446541
We observe the distribution of odd and even elements in the gap set of a numerical semigroup. For embedding dimension 2 or 3 and depending on the number of odd minimal generators of a numerical semigroup S, we compute O(G(S))−E(G(S)), the difference between the number of odd and even elements in the gap set. We also obtain the results on O(G(S))−E(G(S)) when the minimal generators of S are one of the followings: some compound sequences, a geometric sequence, or an arithmetic sequence.