{"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/majorization-and-inequalities-among-complete","title":"Majorization and Inequalities among Complete Homogeneous Symmetric Functions","arxiv_id":"2505.08149","date":"2025-05-13","proceeding":null,"authors":["Jia Xu","Yong Yao"],"abstract":"Inequalities among symmetric functions are fundamental in various branches of mathematics, thus motivating a systematic study of their structure. Majorization has been shown to characterize inequalities among commonly used symmetric functions, except for complete homogeneous symmetric functions (shortened as CHs). In 2011, Cuttler, Greene, and Skandera posed a natural question: Can majorization also characterize inequalities among CHs? Their work demonstrated that majorization characterizes inequalities among CHs up to degree 7 and suggested exploring its validity for higher degrees. In this paper, we show that, for every degree greater than 7, majorization does not characterize inequalities among CHs.","url_abs":"https://arxiv.org/abs/2505.08149v3","url_pdf":"https://arxiv.org/pdf/2505.08149v3.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":"majorization-and-inequalities-among-complete","repo_url":"https://github.com/xuyao7/computaion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}