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: Erdős–Ko–Rado-type theorems on permutations | Statement: [Erdős–Ko–Rado theorem, hasGeneralization, Erdős–Ko–Rado-type theorems on permutations]

Target entity: Erdős–Ko–Rado-type theorems on permutations
Context triple: [Erdős–Ko–Rado theorem, hasGeneralization, Erdős–Ko–Rado-type theorems on permutations]

• A. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• B. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• C. Foundations of Combinatorial Theory
  Foundations of Combinatorial Theory is a seminal mathematical work by Gian-Carlo Rota that helped establish modern combinatorics as a rigorous and unified field of study.
• D. Alon–Tarsi conjecture
  The Alon–Tarsi conjecture is a prominent open problem in combinatorics and graph theory concerning orientations and colorings of graphs, with deep connections to Latin squares and polynomial method techniques.
• E. Sperner family
  A Sperner family is a collection of subsets of a finite set in which no subset is contained within another, central in extremal set theory and combinatorics.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Erdős–Ko–Rado-type theorems on permutations
Target entity description: Erdős–Ko–Rado-type theorems on permutations are results in extremal combinatorics that determine the maximum size and structure of families of permutations with prescribed intersection properties.

• A. Erdős–Ko–Rado theorem chosen
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• B. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• C. Foundations of Combinatorial Theory
  Foundations of Combinatorial Theory is a seminal mathematical work by Gian-Carlo Rota that helped establish modern combinatorics as a rigorous and unified field of study.
• D. Alon–Tarsi conjecture
  The Alon–Tarsi conjecture is a prominent open problem in combinatorics and graph theory concerning orientations and colorings of graphs, with deep connections to Latin squares and polynomial method techniques.
• E. Sperner family
  A Sperner family is a collection of subsets of a finite set in which no subset is contained within another, central in extremal set theory and combinatorics.
• F. None of above.