{"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/bohemian-upper-hessenberg-toeplitz-matrices","title":"Bohemian Upper Hessenberg Toeplitz Matrices","arxiv_id":"1809.10664","date":"2018-09-27","proceeding":null,"authors":["Eunice Y. S. Chan","Robert M. Corless","Laureano Gonzalez-Vega","J. Rafael Sendra","Juana Sendra","Steven E. Thornton"],"abstract":"We look at Bohemian matrices, specifically those with entries from $\\{-1, 0, {+1}\\}$. More, we specialize the matrices to be upper Hessenberg, with subdiagonal entries $1$. Even more, we consider Toeplitz matrices of this kind. Many properties remain after these specializations, some of which surprised us. Focusing on only those matrices whose characteristic polynomials have maximal height allows us to explicitly identify these polynomials and give a lower bound on their height. This bound is exponential in the order of the matrix.","url_abs":"http://arxiv.org/abs/1809.10664v1","url_pdf":"http://arxiv.org/pdf/1809.10664v1.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":"bohemian-upper-hessenberg-toeplitz-matrices","repo_url":"https://github.com/BohemianMatrices/Bohemian_Upper_Hessenberg_Toeplitz_Matrices","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}