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Diskr. Mat., 2020, Volume 32, Issue 2, Pages 3–14 (Mi dm1594)  

On the numerical semigroup generated by $\{b^{n+1+i}+\frac{b^{n+i}-1}{b-1}\mid i\in\mathbb{N}\}$

Ze Gu

School of Mathematics and Statistics, Zhaoqing University

Abstract: Let $b, n$ be two positive integers such that $b\geq 2$, and $S(b,n)$ the numerical semigroup generated by $\{b^{n+1+i}+\frac{b^{n+i}-1}{b-1}\mid i\in\mathbb{N}\}$. Applying two order relations, we give formulas for computing the embedding dimension, the Frobenius number, the type and the genus of $S(b,n)$.

Keywords: Numerical semigroups; embedding dimension; Frobenius number; pseudo-Frobenius number; genus.

Funding Agency Grant Number
National Natural Science Foundation of China 11701504


DOI: https://doi.org/10.4213/dm1594

Full text: PDF file (489 kB)
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UDC: 512.533.8
Received: 22.10.2019

Citation: Ze Gu, “On the numerical semigroup generated by $\{b^{n+1+i}+\frac{b^{n+i}-1}{b-1}\mid i\in\mathbb{N}\}$”, Diskr. Mat., 32:2 (2020), 3–14

Citation in format AMSBIB
\Bibitem{Gu20}
\by Ze~Gu
\paper On the numerical semigroup generated by $\{b^{n+1+i}+\frac{b^{n+i}-1}{b-1}\mid i\in\mathbb{N}\}$
\jour Diskr. Mat.
\yr 2020
\vol 32
\issue 2
\pages 3--14
\mathnet{http://mi.mathnet.ru/dm1594}
\crossref{https://doi.org/10.4213/dm1594}


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