Majorization and Inequalities among Complete Homogeneous Symmetric Functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917423791210496 |
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| author | Xu, Jia Yao, Yong |
| author_facet | Xu, Jia Yao, Yong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08149 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Majorization and Inequalities among Complete Homogeneous Symmetric Functions Xu, Jia Yao, Yong Symbolic Computation Algebraic Geometry Combinatorics 05E05, 14P99, 68W30 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. |
| title | Majorization and Inequalities among Complete Homogeneous Symmetric Functions |
| topic | Symbolic Computation Algebraic Geometry Combinatorics 05E05, 14P99, 68W30 |
| url | https://arxiv.org/abs/2505.08149 |