# On the numerical semigroup generated by {bn+1+i+bn+i−1b−1∣i∈N} $\begin{array}{} \{b^{n+1+i}+\frac{b^{n+i}-1}{b-1}\mid i\in\mathbb{N}\} \end{array}$

Authors
• 1 Zhaoqing University, Guangdong , (China)
Type
Published Article
Journal
Discrete Mathematics and Applications
Publisher
De Gruyter
Publication Date
Aug 14, 2020
Volume
30
Issue
4
Pages
257–264
Identifiers
DOI: 10.1515/dma-2020-0022
Source
De Gruyter
Keywords
Let b, n be two positive integers such that b ≥ 2, and S(b, n) be the numerical semigroup generated by {bn+1+i+bn+i−1b−1∣i∈N} $\begin{array}{} \{b^{n+1+i}+\frac{b^{n+i}-1}{b-1}\mid i\in\mathbb{N}\} \end{array}$. Applying two order relations, we give formulas for computing the embedding dimension, the Frobenius number, the type and the genus of S(b, n).