{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/boundaries-of-the-amplituhedron-with","title":"Boundaries of the Amplituhedron with amplituhedronBoundaries","arxiv_id":"2002.07146","date":"2020-02-17","proceeding":null,"authors":["Tomasz Lukowski","Robert Moerman"],"abstract":"Positive geometries provide a modern approach for computing scattering amplitudes in a variety of physical models. In order to facilitate the exploration of these new geometric methods, we introduce a Mathematica package called ``amplituhedronBoundaries'' for calculating the boundary structures of three positive geometries: the amplituhedron $\\mathcal{A}_{n,k}^{(m)}$, the momentum amplituhedron $\\mathcal{M}_{n,k}^{(m)}$ and the hypersimplex $\\Delta_{k,n}$. The first two geometries are relevant for scattering amplitudes in planar $\\mathcal{N}=4$ SYM, while the last one is a well-studied polytope appearing in many contexts in mathematics, and is closely related to $\\mathcal{M}_{n,k}^{(2)}$. The package includes an array of useful tools for the study of these positive geometries, including their boundary stratifications, drawing their boundary posets, and additional tools for manipulating combinatorial structures useful for positive Grassmannians.","url_abs":"https://arxiv.org/abs/2002.07146v1","url_pdf":"https://arxiv.org/pdf/2002.07146v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"boundaries-of-the-amplituhedron-with","repo_url":"https://github.com/mrmrob003/amplituhedronBoundaries","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}