Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: LYM inequality | Statement: [Sperner family, relatedConcept, LYM inequality]

Target entity: LYM inequality
Context triple: [Sperner family, relatedConcept, LYM inequality]

• A. Hardy–Littlewood–Pólya inequality
  The Hardy–Littlewood–Pólya inequality is a fundamental result in majorization theory and inequalities that characterizes how convex functions behave under rearrangements of sequences or vectors.
• B. Brunn–Minkowski inequality
  The Brunn–Minkowski inequality is a fundamental result in convex geometry and analysis that relates the volumes of sets in Euclidean space to the volume of their Minkowski sum, underpinning many isoperimetric and functional inequalities.
• C. Muirhead's inequality
  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.
• D. 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.
• E. Riesz rearrangement inequality
  The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: LYM inequality
Target entity description: The LYM inequality is a fundamental result in extremal set theory that bounds the size of an antichain in a finite Boolean lattice by relating it to binomial coefficients.

• A. Hardy–Littlewood–Pólya inequality
  The Hardy–Littlewood–Pólya inequality is a fundamental result in majorization theory and inequalities that characterizes how convex functions behave under rearrangements of sequences or vectors.
• B. Brunn–Minkowski inequality
  The Brunn–Minkowski inequality is a fundamental result in convex geometry and analysis that relates the volumes of sets in Euclidean space to the volume of their Minkowski sum, underpinning many isoperimetric and functional inequalities.
• C. Muirhead's inequality
  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.
• D. 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.
• E. Riesz rearrangement inequality
  The Riesz rearrangement inequality is a fundamental result in mathematical analysis that provides an optimal bound for integrals of products of functions in terms of their symmetric decreasing rearrangements.
• F. None of above. chosen