Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study Muirhead-type generalizations of families of inequalities due to Newton, Maclaurin and others. Each family is defined in terms of a commonly used basis of the ring of symmetric functions in n variables. Inequalities corresponding to elementary symmetric functions and por sum symmetric functions are characterized by the same simple poset which generalizes the majorization order. Some analogous results are also obtained for the Schur, homogeneous, and monomial cases.
['Allison Cuttler', 'Curtis Greene', 'Mark Skandera']
I am writing a research paper on a idea Inequalities for symmetric means
[{"from": "human", "value": "I am writing a research paper on a idea Inequalities for symmetric means"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study Muirhead-type generalizations of families of inequalities due to Newton, Maclaurin and others. Each family is defined in terms of a commonly used basis of the ring of symmetric functions in n variables. Inequalities corresponding to elementary symmetric functions and por sum symmetric functions are characterized by the same simple poset which generalizes the majorization order. Some analogous results are also obtained for the Schur, homogeneous, and monomial cases."}]