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- Publisher
- Springer Journals
- Copyright
- Copyright © The Hebrew University of Jerusalem 2021
- ISSN
- 0021-2172
- eISSN
- 1565-8511
- DOI
- 10.1007/s11856-021-2263-5
- Publisher site
- See Article on Publisher Site
Abstract
Let ℒ∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\cal L}^ \ast}$$\end{document} be a family of finite subsets of ℕ0 having the following properties.{0}, {1}∈ℒ∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\{ 1\} \in {{\cal L}^ \ast }$$\end{document} and all other sets of ℒ∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\cal L}^ \ast}$$\end{document} lie in ℕ≥2.If L1, L2∈ℒ∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${L_2} \in {{\cal L}^ \ast}$$\end{document}, then the sumset L1+L2={l1+l2l1∈L1l2∈L2}∈ℒ∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${L_1} + {L_2} = \{ {l_1} + {l_2}:{l_1} \in {L_1},{l_2} \in {L_2}\} \in {{\cal L}^ \ast }$$\end{document}.We show that there is a Dedekind domain D whose system of sets of lengths equals ℒ∗\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${{\cal L}^ \ast}$$\end{document}.
Journal
Israel Journal of Mathematics – Springer Journals
Published: Apr 1, 2022