Muirhead's inequality
E1247124
UNEXPLORED
Muirhead's inequality is a fundamental result in symmetric inequalities that compares sums of symmetric power terms of variables based on majorization of exponent sequences.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Muirhead's inequality canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T17020132 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Muirhead's inequality Context triple: [Karamata's inequality, usedToDerive, Muirhead's inequality]
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A.
Karamata's inequality
Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
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B.
Chebyshev’s sum inequality
Chebyshev’s sum inequality is a mathematical inequality that provides bounds on the sum of products of similarly ordered sequences, widely used in analysis and probability theory.
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C.
Maclaurin’s inequality in symmetric means
Maclaurin’s inequality in symmetric means is a classical result in mathematical analysis that relates and bounds the sequence of elementary symmetric means of a set of nonnegative real numbers, showing they form a decreasing sequence.
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D.
Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
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E.
Muirhead
Muirhead is a Scottish surname, historically associated with families from areas characterized by moorland or "muir" landscapes.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Muirhead's inequality Target entity description: Muirhead's inequality is a fundamental result in symmetric inequalities that compares sums of symmetric power terms of variables based on majorization of exponent sequences.
-
A.
Karamata's inequality
Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
-
B.
Chebyshev’s sum inequality
Chebyshev’s sum inequality is a mathematical inequality that provides bounds on the sum of products of similarly ordered sequences, widely used in analysis and probability theory.
-
C.
Maclaurin’s inequality in symmetric means
Maclaurin’s inequality in symmetric means is a classical result in mathematical analysis that relates and bounds the sequence of elementary symmetric means of a set of nonnegative real numbers, showing they form a decreasing sequence.
-
D.
Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality is a fundamental result in linear algebra and analysis that bounds the inner product of two vectors by the product of their magnitudes, underpinning many concepts in geometry, probability, and functional analysis.
-
E.
Muirhead
Muirhead is a Scottish surname, historically associated with families from areas characterized by moorland or "muir" landscapes.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.