Betti elements and catenary degree of telescopic numerical semigroup family
Abstract
The catenary degree is an invariant that measures the distance between factorizations of elements within a numerical semigroup. In general, all possible catenary degrees of the elements of the numerical semigroups occur as the catenary degree of one of its Betti elements. In this study, Betti elements of some telescopic numerical semigroup families with embedding dimension three were found and formulated. Then, with the help of these formulas, Frobenius numbers and genus of these families were obtained. Also, the catenary degrees of telescopic numerical semigroups were found with the help of factorizations of Betti elements of these semigroups.
- Published
- 18 May 2021
- Volume
- 2021 (2021)
- License
- CC BY 3.0
Copyright © 2021 Meral Suer, Mehmet Sirin Sezgin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
M. Suer, M. S. Sezgin, Betti elements and catenary degree of telescopic numerical semigroup family, Algebra Lett. 2021 (2021), 3. https://doi.org/10.28919/al/5466
BibTeX
@article{Suer2021,
author = {Suer, Meral and Sezgin, Mehmet Sirin},
title = {Betti elements and catenary degree of telescopic numerical semigroup family},
journal = {Algebra Lett.},
volume = {2021},
year = {2021},
pages = {3},
doi = {10.28919/al/5466}
}